Probability Game Ideas Part 2
THE JEOPARDY GAME
Instructions/Mechanics of the game:
1. Divide 2 or more players into two or more teams.
2. Choosing Category:
● Teams take turns selecting a category from the game board.
● Each category has five (5) point values (random), and each corresponds to a question
3. Answering Questions:
● After selecting a category and a specific point value, the team has a limited time to buzz in and provide their answer to the question that is in the point value they selected
● If the team answers correctly, they earn the corresponding points.
● If the team answers incorrectly, they lose the corresponding points.
4. Winning:
● The team with the highest total score at the end of the Final Jeopardy round wins.
SOLUTION SHEET #1
Question 1:
What is the probability that a player chooses a prime number for their point value in the category, “Probability”?
Solution:
n (S) = 5
n (prime number) = 3
P (prime number) = 3/5 [wherein 3 = no. of favorable outcomes & 5 = no. of all possible outcomes]
Question 2:
What is the probability that a player chooses a composite number for their point value across all three categories?
Solution:
n (S) = 15
n (composite number) = 8
P (composite number) = 8/15 [wherein 8 = no. of favorable outcomes & 15 = no. of all possible outcomes]
Question 3:
What is the probability that a player chooses a number that ends in zero (0) for their point value across all three categories?
Solution:
n (S) = 15
n (composite number) = 5
P (composite number) = 5/15 ---> 1/3 [wherein 5 = no. of favorable outcomes & 15 = no. of all possible outcomes]
Question 4:
What is the probability that a player chooses a number divisible to three (3) for their point value in the “Experimental/Theoretical Probability” category?
Solution:
n (S) = 5
n (divisible to 3) = 2
P (divisible to 3) = 2/5 [wherein 2 = no. of favorable outcomes & 5 = no. of all possible
outcomes]
Question 5:
What is the probability that a player chooses an even number as their point value in the categories, “Probability” and “Experimental/Theoretical Probability”?
Solution:
n (S) = 10
n (composite number) = 6
P (composite number) = 6/10 ---> 3/5 [wherein 6 = no. of favorable outcomes & 10 = no. of all possible outcomes]
SOLUTION SHEET #2
Category (PROBABILITY)
Question 1: Which method uses line segments to list and enumerate all the possible outcomes?
Answer: TREE DIAGRAM
Question 2: Which method uses the technique of multiplying the numbers to get the total number of ways?
Answer: FUNDAMENTAL COUNTING PRINCIPLE
Question 3: What type of probability uses trials?
Answer: EXPERIMENTAL THEORY
Question 4: What do you call a set of outcomes of an experiment?
Answer: SAMPLE SPACE
Question 5: What is the individual outcome in a sample space?
Answer: SAMPLE POINT
Category (EXPERIMENTAL OR THEORETICAL)
Question 1: In a game of Russian Roulette, you spin the cylinder a total of 3 times on a revolver with a total of 7 chambers. What is the probability that the loaded chamber will fire?
Answer: EXPERIMENTAL
Question 2: In a game of cards with 52 total cards, what is the probability of you pulling a red card?
Answer: THEORETICAL
Question 3: What is the probability of you getting a number of 5 in a game of rolling a dice?
Answer: THEORETICAL
Question 4: What is the probability of you getting an even number when you roll a dice a total of 2 times?
Answer: EXPERIMENTAL
Question 5: In a game of cards, what is the probability of you pulling a face card when you pull a card 5 times?
Answer: EXPERIMENTAL
Category (SOLVING)
Question 1: In a game of Russian Roulette, you spin the cylinder a total of 3 times on a revolver with a total of 7 chambers. What is the probability that the loaded chamber will fire?
Solution:
n (S) = 7
n (chamber) = 3
P (chamber) = 3/7 [3 = favorable outcomes & 7 = all possible outcomes]
Question 2: In a game of cards with 52 total cards, what is the probability of you pulling a red card?
Solution:
n (S) = 52
n (red cards) = 26
P (red cards) = 26/52 ---> 1/2 [26 = favorable outcomes & 52 = all possible outcomes]
Question 3: What is the probability of you getting a number of 5 in a game of rolling a dice?
Solution:
n (S) = 6
n (5) = 1
P (5) = 1/6 [1 = favorable outcomes & 6 = all possible outcomes]
Question 4: What is the probability of you getting an even number when you roll a dice?
Solution:
n (S) = 6
n (even number) = 2
P (even number) = 2/6 ---> 1/3 [2 = favorable outcomes & 6 = all possible outcomes]
Question 5: In a game of cards, what is your probability of pulling a face card?
Solution:
n (S) = 52
n (face card) = 12
P (face card) = 12/52 ---> 3/13 [12 = favorable outcomes & 52 = all possible outcomes]
Spin Pop Game
.png "Spin Pop")
Mechanics:
1. The game will host 1-5 players.
2. The game will include a wheel of questions, darts, and 100 balloons.
3. Each player will get the chance to spin the wheel once. The wheel will have 9 slices, representing 9 different question difficulties.
4. There will be 3 question difficulties represented by a color; green, orange, and red.
a. If a player lands on a:
i. Green Slice
- The player will be given an easy-difficulty question to answer.
- If they answered correctly, they will be given 15 chances to pop a balloon.
ii. Orange Slice
- The player will be given a medium-difficulty question to answer.
- If they answered correctly, they will be given 18 chances to pop a balloon.
iii. Red Slice
- The player will be given a hard-difficulty question to answer.
- If they answered correctly, they will be given 25 chances to pop a balloon.
5. If their answer is correct, they will be given a chance or more to pop one or more balloon/s.
6. The game will continue until all balloons are popped.
7. If a player still has a chance to pop a balloon after all balloons are popped, the remaining chances will be considered a popped balloon.
Points System:
1. If a player pops 10-20 balloons:
- They may choose any of the small-sized prizes available.
2. If a player pops 21-49 balloons:
- They may choose any of the medium-sized prizes available.
3. If a player pops 50-100 balloons:
- They may choose any of the large-sized prizes available.
SOLUTION SHEET
Question A: If a player threw 56 darts and popped only 23 balloons, what is the probability of popping a balloon?
Solution: n(p)=56
n(a)=23
23/56 = 41.1%
Question B: If the hard questions were picked 7 times, but only got answered correctly 3 times. What’s the probability of correctly answering the hard questions?
Solution: n(p)=7
n(b)=3
3/7 = 42.857143
TEST YOUR LUCK!
.png "TEST YOUR LUCK")
Instructions/Mechanics of the game:
Pointing system:
- Opening a box with food or money gives one point
-Opening a box with nothing in it will result to a deduction of a point.
-Whoever has the most points by the end of the game gets to keep all rewards while the losers return their
winnings.
STEPS IN PLAYING:
1. The gamemaster will scatter the rewards in all 20 boxes. (The number of empty boxes depends on the number of rewards. Rewards are provided by the players themselves. Commonly food or money, but the amount of money varies depending on the accumulated share from all players. All players are required to give at least 2 rewards, a food item and a certain amount of money, number of players for the game is a minimum of 3 and a maximum of 7)
2. As a player, you will choose a number and answer its corresponding question in order to gain the reward or deduction of the box. (All questions will be about probability and statistics of real-life scenarios)
3. The game will go on until all 20 boxes are opened. (Rotation of turns is counterclockwise. In order to choose who goes first, each player will roll 2 dice and the highest number will be the first to pick a box. In a case of a tie, the players will roll the dice again.)
SOLUTION SHEET
Question 1:
In a game of “Test Your Luck!”, John, Fred and Mark are competing to win their prizes. The accumulated prizes result to 8 boxes with money, 6 with food and 6 with nothing. After rolling the dice, John is the first to choose, followed by Mark. John manages to answer the question of the corresponding box correctly, what is the chance of John gaining a point?
SOLUTION
Favorable Outcomes: 14 (boxes with food or money)
Total Possible outcomes: 20(number of boxes left in the game.).
P = 14 (boxes with food or money) / 20 (total No. of remaining boxes) = 14/20 = 7/10
Answer: The probability (P) of Arvey gaining a point is 7/10
Question 2:
John’s turn resulted to a deduction of a point because the box he chose had nothing in it. Now it was Marks’s turn, after answering the question correctly what is the probability of him losing a point?
SOLUTION
Favorable Outcomes: 5 (Empty boxes)
Total Possible outcomes: 19(number of boxes left in the game).
P = 5 (Empty boxes) / 19 (total No. of remaining boxes) = 5/19
Answer: The probability (P) of Vaughn losing a point is 5/19
Question 3:
Mark’s turn resulted to him gaining a point through a food box. It is now Fred’s turn, she is only aiming for money boxes. After answering the problem correctly, what is the probability Fred not picking a money box.
SOLUTION
Favorable Outcomes: 10 (Food or empty boxes.)
Total Possible outcomes: 18(number of boxes left in the game.).
P = 10 (Food or empty boxes) / 18 (total No. of remaining boxes) = 10/18 = 5/9
Answer: The probability (P) of Fred not picking a money box is 5/9
Question 4:
Fred successfully picks a money box. John is looking to make up for his deduction of a point. Assuming he answers the question correctly, what is the probability of him gaining a point?
SOLUTION
Favorable Outcomes: 12 (Food or money boxes.)
Total Possible outcomes: 17(number of boxes left in the game.).
P = 12 (boxes with food or money) / 17 (total No. of remaining boxes) = 12/17
Answer: The probability (P) of John gaining a point is 12/17.
Question 5:
John finally gains a point by choosing a money box, but Mark is looking to steal the lead. He is feeling hungry, so he hopes for a food box. Mark answers his question correctly. What is the probability of Mark not getting a food box?
SOLUTION
Favorable Outcomes: 11 (money or empty boxes.)
Total Possible outcomes: 16(number of boxes left in the game.).
P = 11 (boxes with food or money) / 16 (total No. of remaining boxes) = 11/16
Answer: The probability (P) of Fred not picking a money box is 11/16
Question 6:
Mark unfortunately picks an empty box. This results to a deduction of a point and equalizes John and Mark. Fred is looking to extend her lead. She is aiming for a point. Assuming she answers correctly, what is the probability of her gaining a point?
SOLUTION
Favorable Outcomes: 10 (Food or money boxes.)
Total Possible outcomes: 15(number of boxes left in the game.).
P = 10 (boxes with food or money) / 15 (total No. of remaining boxes) = 10/15 = 2/3
Answer: The probability (P) of Fred gaining a point is 2/3
Question 7:
Unfortunately, Fred answers incorrectly so she does not get to open the contents of her chosen box. It is now John’s turn. John is looking to tie the lead as well, but needs money to get home. He is aiming for a money box. John answers his question correctly. What is the probability of him picking a money box?
SOLUTION
Favorable Outcomes: 6 (money boxes.)
Total Possible outcomes: 15(number of boxes left in the game.).
P = 6 (boxes money) / 15 (total No. of remaining boxes) = 6/15 = 2/5
Answer: The probability (P) of John getting a money box is 2/5
Question 8:
John ties the lead by choosing a money box. Mark is still looking for food boxes. Mark answers his question correctly. What is the probability of him choosing a food box?
SOLUTION
Favorable Outcomes: 5 (Food boxes.)
Total Possible outcomes: 14(number of boxes left in the game.).
P = 5 (boxes with food) / 14 (total No. of remaining boxes) = 5/14
Answer: The probability (P) of Mark choosing a food box is 5/14
Question 9:
Mark unfortunately chose another empty box, resulting for his score to be -1. Fred has the chance to gain the lead from John. After answering correctly, she aims for a point. What is the probability of her losing a point?
SOLUTION
Favorable Outcomes: 10 (Food or money boxes.)
Total Possible outcomes: 13(number of boxes left in the game.).
P = 10 (boxes with food or money) / 13 (total No. of remaining boxes) = 10/13
Answer: The probability (P) of Fred gaining a point is 10/13
Question 10:
Fred gains a point through a food box. Assuming John answers his next question correctly, what is his chance to equalize his points with Fred?
SOLUTION
Favorable Outcomes: 9 (Food or money boxes.)
Total Possible outcomes: 18(number of boxes left in the game.).
P = 9 (boxes with food or money) / 12 (total No. of remaining boxes) = 9/12 = 3/4
Answer: The probability (P) of John equalizing points with Fred is 3/4.
BOMBA NA!
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Instructions/Mechanics of the game:
* To pop the balloon using a dart, and answer the question inside the balloon to win a prize.
1. The player will be given 3 darts to shoot at the balloons.
2. There will be 10 balloons with different sizes, ranging from largest to smallest. (Largest – Easy ; Smallest– Difficult)
3. When a balloon is popped, the player shall answer the question (about probability) inside to win the prize. The smaller the balloon popped and the more difficult the question answered, the bigger the prize.
4. If the player hits a balloon and answers the question, they will be allowed to shoot with their remaining darts.
5. The player will be given 3 darts, after 3 tries if the player does not hit any, the next player shall play.
6. Prizes will be awarded after all 3 darts have been used, with the size of the popped balloon determining the prize.
SOLUTION SHEET
Question 1: If you had 2 red marbles, and 3 blue marbles, what is the probability that you will pick a blue marble?
n(s) = 5 n(blue marble) = 3 P(blue marble) = 3/5
Question 2: There is a class of 25 with 15 girls and 10 boys, what is the probability of the teacher choosing a boy to present?
n(25) = 25 n(boys) = 10 P(boys) = 2/5
Question 3: You roll a six-sided dice. What is the probability of getting a prime number?
n(s) = 6 n(prime numbers) = 3 P(prime numbers) = 1/2
Question 4: You flip 2 coins, what is the probability of getting both heads?
n(s) = 4, n(both heads) = 1 P(both heads) = 1/4
Question 5: You roll a six-sided dice. What is the probability of getting a perfect square number?
n(s) = 6, n(perfect square numbers) = 2 p(prime numbers) = 1/3
Question 6: Kate has 20 dresses: 6 blue, 9, pink and 5 yellow. What is the probability that she will pick a yellow dress ?
n(s) = 20, n(yellow dress) = 5 P(yellow dress) = 1/4
Question 7: In a deck of 52 cards, what is the probability of getting a spade?
n(s) = 52, n(spade) = 13 P(spade) = 1/4
Question 8: In a deck of 52 cards, what is the possibility of getting a king and queen card?
n(s) = 52, n(king and queen) = 8, P(king and queen) = 2/13
Question 9: There is a shop that sells 24 t-shirts, 15 pants and 6 shoes, and 3 rings. What is the probability of a customer buying neither pants nor shoes?
Given:
n(s) = 48
n(pants) = 15
n(shoes) = 6
n(total) = n(pants) + n(shoes)
= 15 + 6 = 21
n(neither pants nor shoes) = n(s) - n(total)
= 48 - 21 = 27
P(neither pants nor shoes) = 9/16
Question 10: In a deck of 52 cards, what is the probability of getting neither a face card nor an ace?
n(s) = 52
n(face cards) = 12
n(aces) = 4
n(total) = n(face cards) + n(aces)
= 12 + 4 = 16
n(neither fc, a) = n(s) - n(total)
= 52 - 16 = 36
P(neither fc, a) = 9/13
