Question

(1) Consider an experiment in which a coin is flipped and a ball is chosen from a bag that contains balls of three different colors: green, orange, and purple. The experimenter records the side of the coin that comes up and the color of the chosen ball.

(a) What is the outcome space for this experiment? Write it as a set.

(b) Do you know whether all the outcomes are equally likely based on the information

given in this problem? Why or why not?

(2) Suppose we have three events: A, B, and C. We know that P(A) = .43, P(B) = .44, andP(C) = .19. We further know that B and C are mutually exclusive but that P(A∩B) = .07 and P(A ∩ C) = .13.

(a) What is P(A ∪ B)? (b) What is P(A′ ∩B′)?

(c) WhatisP(A∪B∪C)?

Answer 1

1)

a) Outcome space for coin flip, S= {Heads, Tails}

Outcome space for ball chosen from bag, S = {Green, Orange, Purple}

b)

The outcome of the single coin flip is eqally likely P(coin is head) = P(coin is tails) = 0.5

If the bag contains equal number of green, orange and purple balls then the outcome is equally likely P(green) = P(orange) = P(purple) = 0.333.

If the bag contains unequal number of green, orange and purple balls then the outcome is dependent on the distribution of the different colored balls.

2)

a) P(A B) = P(A) + P(B) - P(A B) = 0.43 + 0.44 - 0.07 = 0.8

b) P(A' B')= 1 -  P(A B) = 1 - 0.8 = 0.2

c)  P(A B C ) = P(A) + P(B) + P(C) - P(AB) - P(AC) - P(BC) +P(ABC)

= 0.43+0.44+0.19 - 0.07 - 0.13 - 0 + 0

= 0.67