Question

A radio station has movie tickets to give away: 4 for a new action movie, 5 for a comedy movie, and 3 for a sci-fi movie. The disc jockey reaches into a box to randomly pick tickets as people call in. What is the probability that the first caller will receive a ticket to the comedy and the second will receive a ticket to the action movie?

Answer 1

0.152

Explanation:

To calculate the probability that the first caller will receive a ticket to the comedy (5 options) and the second will receive a ticket to the action movie (4 options), you can use the multiplication rule for independent events.

Probability of the first caller receiving a comedy ticket = 5/12 (since there are 5 comedy tickets out of a total of 12 tickets).

Now, after the first caller has received a comedy ticket, there are 4 comedy tickets and 11 tickets left in the box.

Probability of the second caller receiving an action movie ticket = 4/11 (since there are 4 action movie tickets out of the remaining 11 tickets).

To find the probability that both of these events happen together (i.e., the first caller gets a comedy ticket and the second caller gets an action movie ticket), multiply the probabilities:

(5/12) * (4/11) = (20/132) = 5/33

So, the probability that the first caller will receive a ticket to the comedy, and the second will receive a ticket to the action movie is 5/33. Which in decimal form is 0.1515, which rounded up is 0.152

Answer 2

5/33

Explanation:

Probability of first caller (comedy) = 5/(3+4+5) = 5/12

Probability of second caller (action) = 4/(3+4+4) = 4/11

Probability of both = 5/12 * 4/11 = 5/33