This document describes 6 games with probabilities of winning: 1. Balloon darts game - Probability of popping a balloon is 1/2. 2. Cola ring toss game - Probability of landing a ring on a bottle is 1/2. 3. High striker game - Probability of hitting the highest height is 3/5. 4. Cards game - Probability of drawing an ace is 1/13 and drawing a diamond is 1/4. 5. Apple eating game - Probability of a pair finishing an apple in under 1 minute is 1/5. 6. Snakes and ladders game - Probability of getting a snake in one roll is 1/6 and 7

1. FARE-GAME PLANNER
Submitted by: Sasha Bettina R. Quinitip

2. Game 1: Balloon darts
Probability to pop a balloon if you are given
three darts and win a prize
Player Balloon’s popped Darts
A 3 3
B 1 3
C 2 3
D 0 3
6 12
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟𝑠
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
𝑃 =
(3 + 1 + 2 + 0)
(3 + 3 + 3 + 3)
𝑃 =
6
12
or ½

3. Game 2: Cola Ring Toss
Probability to land a bottle given five rings and win a
prize
Player Rings successfully landed on a
bottle/s
Tries
A 5 5
B 1 5
C 2 5
D 0 5
E 4 5
F 3 5
15 30
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟𝑠
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
𝑃 =
(5 + 1 + 2 + 0 + 4 + 3)
(5 + 5 + 5 + 5 + 5 + 5)
𝑃 =
15
30
or ½

4. Game 3: High striker
Probability to hit the highest height and win a
prize
Player height Tries
A 5 ft. 1
B 1 ft. 1
C 2 ft. 1
D 4 ft. 1
E 3 ft. 1
15 5
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 𝑜𝑐𝑐𝑢𝑟𝑠
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
𝑃 =
(5 + 1 + 2 + 4 + 3)
(1 + 1 + 1 + 1 + 1 + 1)
𝑃 =
15
5
or 3

5. THANK YOU FOR YOUR ATTENTION

6. Game 4: Cards
If a card is drawn from an ordinary deck, find the
probability of drawing
1. An ace
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑃 =
4 𝑎𝑐𝑒
52 𝑐𝑎𝑟𝑑𝑠
(lowest term divisible by 4)
𝑃 =
1
13
Probability of drawing the ace to win the game

7. 2. A diamond
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑃 =
13 𝑑𝑖𝑎𝑚𝑜𝑛𝑑𝑠
52 𝑐𝑎𝑟𝑑𝑠
(lowest terms divisible
by 13)
𝑃 =
1
4
Probability of drawing the diamond to win
the game

8. Game 5: Eating apple
Find the probability of a pair to finish eating the apple in
less than 1 minute to win the game.
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑃 =
1 𝑝𝑎𝑖𝑟 𝑖𝑛 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑜𝑛𝑒 𝑚𝑖𝑛𝑢𝑡𝑒
5 𝑝𝑎𝑖𝑟𝑠
𝑃 =
1
5
Probability of that 1 pair to finish eating that apple in less
than 1 minute

9. Game 6: Snakes and ladders
1.Find the probability of getting the snake in one throw
of the dice
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑃 =
1 𝑡ℎ𝑟𝑜𝑤
6 𝑟𝑜𝑙𝑙𝑠
𝑃 =
1
6

10. 2. Find the probability of getting the snake
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑃 =
7 𝑠𝑛𝑎𝑘𝑒𝑠
36 𝑡ℎ𝑟𝑜𝑤𝑠
𝑃 =
7
36

11. 3. Find the probability of getting the ladder in 1
throw
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑃 =
1 𝑡ℎ𝑟𝑜𝑤
6 𝑟𝑜𝑙𝑙𝑠
𝑃 =
1
6

12. 4.Find the probability of getting the ladder
𝑃 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑃 =
9 𝑙𝑎𝑑𝑑𝑒𝑟𝑠
36 𝑡ℎ𝑟𝑜𝑤𝑠
𝑃 =
9
36
or ¼