Combinations and Probability

Question 1

Show your work and draw box(es) around your final answer(s). Use algebraic methods unless otherwise stated.

A class of 25 students has 13 men and 12 women. A group of 4 students is being chosen to represent the class in a panel discussion. Determine how many different groups could be chosen with the following additional conditions:

a) there are no additional conditions b) there must be exactly two men and exactly two women in the group c) there must be at least one man in the group

Question 2

Show your work and draw box(es) around your final answer(s). Use algebraic methods unless otherwise stated.

About 8% of men and 0.5% of women see no difference between the colours red and green (colour blindness).

a) What are the odds in favour of a randomly-selected male being colour blind? Write as a lowest whole number ratio. b) What are the odds against a randomly-selected woman being colour blind? Write as a lowest whole number ratio. c) What are the odds in favour of a randomly-selected woman being colour blind? Write as a lowest whole number ratio.

Question 3

Show your work and draw box(es) around your final answer(s). Use algebraic methods unless otherwise stated.

Consider a well-shuffled standard deck of 52 cards.

a) Two cards are drawn with replacement from a well-shuffled deck of 52 cards. What is the probability of drawing a queen and then a jack? Use one of the probability equations (shown below) to solve this question. b) Two cards are drawn without replacement from a well-shuffled deck of 52 cards. What is the probability of drawing a king of hearts and then a red card? Use one of the probability equations (shown below) to solve this question. c) One card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a 4 or a black card? Use one of the probability equations (shown below) to solve this question.

P(A B) = P(A) + P(B) P(A B) = P(A) + P(B) P(A B) P(A B) = P(A) P(B) P(A B) = P(A) P(B|A)

Question 4

Show your work and draw box(es) around your final answer(s). Use algebraic methods unless otherwise stated.

In the past two racing seasons Seahorse has won 55% of the time if the track is dry. On rainy days when the track is muddy he has won only 30% of the time. For the next race day there is a 40% chance of rain. What is the probability that Seahorse will win the next race?