drawing a black ball

Probability Level pending

There are 5 5 white and 10 10 black balls in a 1 s t 1^{st} bag, and 20 20 white and 10 10 black balls in a 2 n d 2^{nd} bag. If a bag is selected at random, and then a ball is drawn, find the probability of obtaining a black ball. Give your answer as a decimal number.


The answer is 0.5.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

At any trial, the desired event occurs if either of the following mutually exclusive compound event occur:

I. The first bag is selected, and then a black ball is drawn.

II. The second bag is selected, and then a black ball is drawn.

The probability that the first bag is selected and a black ball is drawn is 1 2 ( 10 15 ) = 1 3 \dfrac{1}{2}\left(\dfrac{10}{15}\right)=\dfrac{1}{3} .

The probability that the second bag is selected and a black ball is drawn is 1 2 ( 10 30 ) = 1 6 \dfrac{1}{2}\left(\dfrac{10}{30}\right)=\dfrac{1}{6} .

The desired probability is 1 3 + 1 6 = 1 2 \dfrac{1}{3}+\dfrac{1}{6}=\dfrac{1}{2} or 0.5 0.5 .

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