Question

the probability distribution table describes rhondas movie collection.
what is the probability that a movie chosen at random is a drama or an action movie?
24%
36%
50%
60%

Explanation:

Step1: Identify the probabilities

The probability of a drama movie \(P(\text{Drama}) = 0.36\) and the probability of an action movie \(P(\text{Action})=0.24\)

Step2: Use the addition rule for mutually - exclusive events

Since a movie can't be both a drama and an action movie at the same time (mutually - exclusive events), the probability \(P(A\cup B)=P(A)+P(B)\). Here \(A\) is the event of choosing a drama movie and \(B\) is the event of choosing an action movie. So \(P(\text{Drama}\cup\text{Action})=P(\text{Drama}) + P(\text{Action})\)

$$P(\text{Drama}\cup\text{Action})=0.36 + 0.24$$

$$P(\text{Drama}\cup\text{Action})=0.6$$

Convert \(0.6\) to a percentage: \(0.6\times100\% = 60\%\)

Answer:

60%