Movie executives collect lots of different data on the movies they show in order to determine who is going to see the different types of movies they produce. This will help them make decisions on a variety of factors from where to advertise a movie to what actors to cast. Below is a two-way frequency table that compares the number of moviegoers who saw Antman to those who saw Mission Impossible: Rogue Nation. 200 people were polled for the survey.

Antman / Mission Impossible: Rogue Nation
Under the age of 30 / 73 / 52
Age 30 or above / 20 / 55

Define each event in the table using the following variables:

A – a person who sawAntman

M – a person who saw Mission Impossible: Rogue Nation

Y – a person under the age of 30

E – a person who is 30 or above

Find the following probabilities. In terms of movie preference, explain what each probability would mean to a movie executive.

1.

2.

3.

4.

5.

6.

7.

8. You roll two dice. The first die shows a ONE and the other die rolls under the table and you cannot see it. What is the probability that you rolled a sum of two?

9. A new bag of golf tees contains 10 red tees, 8 orange tees, 5 green tees and 2 blue tees. You empty the tees into your golf bag.

a. If you randomly choose one tee, what is the probability that it will be orange?

b. If you choose a red tee to use at the first hole and you leave it there, what is the probability that you will choose a red tee to use at the second hole?

10. In a box at the library, there are 8 novels, 10 biographies, and 12 war history books.

a. If you randomly choose one book, what is the probability that it will be a novel?

b. If you randomly choose two books without replacement and the first one is a biography, what is the probability that the second one is a war history book?

11. A new superman MasterCard has been issued to 2000 customers. Of these customers, 1500 hold a Visa card, 500 hold an American Express card and 40 hold a Visa card and an American Express card.

a. Find the probability that a customer chosen at random holds a Visa card, given that the customer holds an American Express card.

b. Find the probability that a customer chosen at random holds an American Express card, given that the customer holds a Visa card.

12. Tim was given the following problem to solve:

“A jar contains 8 black marbles and 4 white marbles. Two marbles are chosen without replacement. What is the probability that the second marble is white, given that the first marble chosen was also white?”

Tim says that the answer is . Is he correct? Why or why not?