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

Answer:

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

Step-by-step explanation:

Conditional Probability

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

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

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?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3}{0.75} = 0.4$

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