Question

At an amusement park, the probability that a child eats popcorn and cotton candy is 0.58. The probability that a child eats popcorn is 0.69 and the probability that a child eats cotton candy is 0.87. What is the probability (rounded to the nearest hundredth) that a child eats cotton candy given that the child has already eaten popcorn

Answer 1

0.84 is the required probability.

Explanation:

We are given the following in the question:

Probability that a child eats popcorn and cotton candy = 0.58

`P(p\cap c) = 0.58`

Probability that a child eats popcorn = 0.69

`P(p) = 0.69`

Probability that a child eats cotton candy = 0.87

`P(c) = 0.87`

We have to evaluate the conditional probability that a child eats cotton candy given that the child has already eaten popcorn.

`P(c|p)\\\\=(P(c\cap p))/(P(p))\\\\=(0.58)/(0.69)\\\\=0.84`

0.84 is the probability that a child eats cotton candy given that the child has already eaten popcorn.