Question

A marble is randomly selected from a bag. The probability of selecting a marble with dots on it is 0.2. The probability of selecting a marble that is both purple and has dots on it is 0.1. What is the probability of selecting a purple marble given that the marble has dots on it? Enter your answer as a decimal in the box.

Answer 1

0.5

Explanation:

Let D be the event of selecting a marble with dots.

Let P be the event of selecting a purple marble.

The probability of selecting a marble with dots, P(D)=0.2

The probability of selecting a marble that is both purple and has dots,
`P(D \cap P)=0.1`

We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)

By the definition of conditional probability:

`P(P|D)= (P(P \cap D))/(P(D)) \\= (0.1)/(0.2)\\ =0.5`

The probability of selecting a purple marble given that the marble has dots on it is 0.5.