Question

the probability that a child watches cartoons after school is 0.56. the probability that the child requests a certain toy of a cartoon character given that the child watches cartoons after school is 0.89. what is the probability that a child will request a toy and watch cartoons after school? give your answer as a percent, rounded to two decimal places if necessary. provide your answer below:

Explanation:

Step1: Recall the multiplication rule for conditional probability

The formula for the probability of two events \( A \) and \( B \) (where \( P(B|A) \) is the probability of \( B \) given \( A \)) is \( P(A \cap B)=P(A)\times P(B|A) \). Let \( A \) be the event that a child watches cartoons after school, and \( B \) be the event that the child requests a certain toy. We know \( P(A) = 0.56 \) and \( P(B|A)=0.89 \).

Step2: Calculate the joint probability

Substitute the values into the formula: \( P(A \cap B)=0.56\times0.89 \).
\( 0.56\times0.89 = 0.4984 \)

Step3: Convert to a percentage

To convert a decimal to a percentage, multiply by 100: \( 0.4984\times100 = 49.84\% \)

Answer:

\( 49.84\% \)