Question

The probability that a toy Raymond picks out of a box is both plush and a dinosaur is 30%. The probability that a toy Raymond picks out of a box is a dinosaur is 75%. What is the probability that a toy that Raymond picks out of a box is plush given that it is a dinosaur?

Answer 1

0.4 = 40% probability that a toy that Raymond picks out of a box is plush given that it is a dinosaur.

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Dinosaur

Event B: Plush.

The probability that a toy Raymond picks out of a box is a dinosaur is 75%.

This means that
`P(A) = 0.75`

The probability that a toy Raymond picks out of a box is both plush and a dinosaur is 30%.

This means that
`P(A \cap B) = 0.3`

What is the probability that a toy that Raymond picks out of a box is plush given that it is a dinosaur?

`P(B|A) = (P(A \cap B))/(P(A)) = (0.3)/(0.75) = 0.4`

0.4 = 40% probability that a toy that Raymond picks out of a box is plush given that it is a dinosaur.