Kyle has 18 purple balls and 2 black balls in a bag. He takes one ball at random from the bag, puts it back, and then takes another ball from the bag.

A tree diagram is drawn to represent this information:
- Probability of drawing a purple ball: $\frac{18}{20}$
- Probability of drawing a black ball: $\frac{2}{20}$

Find the probability that Kyle takes at least one purple ball.

Question

College

Answer :

AngelinaMatthews AngelinaMatthews · Answer 1 · 2023-10-29T14:33:14-04:00

The probability that Kyle takes at least one purple ball is 0.9

Probability is used to measure the likelihood of an event given a set of circumstances.

The probability that Kyle takes at least one purple ball is calculated by the formula P(A) = 1 – P(A’).

In this scenario, A is the event of taking at least one purple ball and A’ is the event of not taking any purple balls.

The probability of taking at least one purple ball (A) is calculated by subtracting the probability of not taking any purple balls (A’) from 1.

There are 20 balls in the bag, 18 of which are purple. This means the probability of not taking any purple balls (A’) is 2/20 = 0.1.

Therefore, the probability of taking at least one purple ball (A) is

1 – 0.1 = 0.9.

In conclusion, the probability that Kyle takes at least one purple ball is 0.9.

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