5.1
Is this game fair? Show using an outcome table and the probabilities.
Two players each toss a 4-sided die. Ann wins if the sum is 5, Marco wins if the sum is 4
The game is not fair
Ann has a 25% chance of winning, Marco has a 18.75% of winning.
The odds in favour are given. Find the probability each event will happen:
a) 3:5
b) 4:1
a) 3/8
b) 4/5
The odds against are given. Find the probability each event will happen:
a) 4:7
b) 10:9
a) 7/11
b) 9/19
A financial institution randomly generates temporary three-digit security codes for the backs of credit cards. Tisa is expecting her credit card to arrive in the mail. Determine the probability that her security code will consist of three different even digits.
Favourable outcomes: 5*4*3
Total outcomes: 10*10*10
Probability: 60/1000 = 6%
Eloise put 7 rubber bracelets in a bag:4 are blue, 1 is pink, 1 is yellow and 1 is striped. Eloise pulls a rubber bracelet without looking.
What is the probability of Eloise pulling a blue rubber bracelet?
4/7
The probability that an event will happen is given. Determine the odds against each event happening.
P(A)= 35%
65:35
(13:7)
Determine the odds in favour of, and the odds against, each event
Tomorrow it will be sunny; 5 of the last 8 days were sunny
Odds in favour:
5:3
Odds against:
3:5
From a committee of 10 people, 3 are randomly chosen to be president, secretary and treasurer. Determine the probability that Jenna, Eli, and Mark will be chosen.
Favourable outcome: 3P3
Total outcomes: 10P3
Probability: 6/720 (0.8%)
Eloise put 7 rubber bracelets in a bag:4 are blue, 1 is pink, 1 is yellow and 1 is striped. Eloise pulls a rubber bracelet without looking.
What is the probability of Eloise pulling a blue, pink or yellow rubber bracelet?
6/7
Determine the odds in favour of, and the odds against, each event
The next traffic light is green; 12 of the last 16 lights were green
Odds in favour-
12:4 (3:1)
Odds against:
4:12 (1:3)
Determine the probability of the coin being a quarter
25%
In the card game Crazy Eights, players are dealt 8 cards from a standard deck of 52 playing cards. Determine the probability that a hand will contain exactly 7 hearts.
Favourable outcomes: 13C7*39C1
Total outcomes:52C8
Probability: 66924/752, 538, 150 (0.0088%)
Is this game fair? Show using an outcome table and the probabilities.
Two players each toss a 4-sided die. Ann wins if the sum is odd, Marco wins if the sum is even
Yes the game is fair.
They both have a 50% chance of winning
Gigi has 16 coins in her pocket and 4 of these coins are quarters. She reaches into her pocket and pulls out a coin at random.
Determine the odds against the coin being a quarter.
12:4
(3:1)
Two brown-eyed parents are told that there is a 25% probability that their baby will have blue eyes. What are the odds in favour of such parents having a baby with blue eyes? What are the odds against?
Odds in favour
1:3
Odds against
3:1
Gwen, Morgan, Arthur, and Kay are volunteering along with 5 other students to be on their school's math team. All the students have equal ability. Determine the probability that Gwen, Morgan, Arthur and Kay along with one other student will be chosen to fill the five spots on the team.
Favourable outcomes: 4C4*5C1
Total outcomes: 9C5
Probability= 5/126 or 3.9%
Is this game fair? Show using an outcome table and the probabilities.
Two players each toss a 4-sided die. Ann wins if the sum is 2, 4, 6 or 8, Marco wins if the sum is 5, no one wins if the sum is 3 or 7.
No the game is not fair.
Ann has a 50% chance of winning, Marco has a 25% chance of winning.
Ear buds are on sale at the local electronics store. The last 7 times ear buds were on sale, they were in stock only 3 times.
Determine the odds in favour of ear buds being in stock this time.
Determine the probability of ear buds NOT being in stock this time.
Odds in favour
3:4
Probability NOT in stock
4/7 or ~57%
Dasha went geocaching and found 6 of the last 11 geocaches she was searching for. In 2 of those cases, she was the first to find the geocache.
Determine the probability that Dasha will find the next geocache she looks for.
Determine the odds against her finding it
Determine the odds in favour of her finding it first
Probability 6/11
Odds against 5:6
Odds in favour of finding it first 2:4 (1:2)
Access to a particular online game is password protected. Every player must create a password that consists of 3 capital letters followed by 2 digits. For each condition below, determine the probability that a password chosen at random will contain the letters A, B and C. Repetitions are allowed.
Favourable outcomes:3*2*1*10*10
Total outcomes:26*26*26*10*10
Probability: 600/1, 757, 600 (0.034%)