Name: Calculator Homework #3 Probability and Counting 1. Suppose: P(A) = 0.4, P(B) = 0.6, and P(A and B) = 0.2. Find the following probabilities. (Use a Venn diagram if needed). Round your answers to 4 decimal places. a) P(A or B) b) P(A and B) c) P(A|B) d) P(A and f?) 2. The table below shows the results of a survey in which 142 men and 145 women workers ages 25 to 64 were asked if they have at least one month's income set aside for emergencies. Round your answers to 4 decimal places. Men Women Total 65 34 149 1 38 61 287 Less than one month's income One month's income or more Total a) Find the probability that a randomly selected worker has one month's income or more set aside for emergencies. b) Given that a randomly selected worker is female, find the probability that the worker has less than one month's income. c) Given that a randomly selected worker has one month's income or more, find the probability that the worker is female. d) Find the probability that a randomly selected worker has less than one month's income saved OR the worker is male. 3. Find the following: a) 10P3 b) 8C3 4. Two cards are selected from a standard deck without replacement. Find the following probabilities. Write your answer as a fraction in lowest terms. a) A face card is selected, then a 7 is selected b) Two face cards are selected 5. A committee of 5 is to be selected from a group of 8 women and 7 men. Find the following probabilities. Round your answers to 4 decimal places. a) The committee consists of 4 women and 1 man b) The committee consists of all men c) The committee consists of at least 1 woman