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? (1 point) 0.139 0.114 0.083 0.152

Explanation:

Step1: Calculate total number of tickets

Total tickets = \(4 + 5+3=12\)

Step2: Calculate probability for first - caller (comedy ticket)

Probability of first - caller getting comedy ticket \(P(C)=\frac{5}{12}\)

Step3: Calculate probability for second - caller (action ticket)

After one comedy ticket is taken, number of tickets left \(n = 11\), number of action tickets \(m = 4\). Probability of second - caller getting action ticket \(P(A)=\frac{4}{11}\)

Step4: Calculate combined probability

Since these are dependent events, combined probability \(P = P(C)\times P(A)=\frac{5}{12}\times\frac{4}{11}=\frac{20}{132}\approx0.152\)

Answer:

0.152