Question

In a city, 49% of the adults are male. Of the adults, 24% are male and rent action-movie DVDs and 10% are female and rent action-movie DVDs. If an adult is randomly picked, the probability that the person rents action-movie DVDs, given that the person is female, is

Answer 1

10%

Step-by-step explanation:

Answer 2

To find the probability that a person rents action-movie DVDs given that the person is female, use conditional probability.

Step-by-step explanation:

To find the probability that a person rents action-movie DVDs given that the person is female, we need to use conditional probability. Conditional probability is the probability of event A occurring given that event B has already occurred.

Let's assign some variables:

• P(M) = probability that an adult is male = 0.49
• P(F) = probability that an adult is female = 1 - P(M) = 0.51
• P(R) = probability that an adult rents action-movie DVDs
• P(R|M) = probability that an adult rents action-movie DVDs given that they are male = 0.24
• P(R|F) = probability that an adult rents action-movie DVDs given that they are female = 0.10

We can use the formula for conditional probability:
P(R|F) = P(R ∩ F) / P(F)

Substituting the given values:
0.10 = P(R ∩ F) / 0.51

Rearranging the equation:
P(R ∩ F) = 0.10 * 0.51

Therefore, the probability that an adult rents action-movie DVDs given that they are female is 0.051 or 5.1%.