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Chapter 2: Q. 2.6 (page 54)

An urn Acontains 3red and3black balls, whereas the urnBcontains 4red and6black balls. If a ball is randomly selected from each urn, what is the probability that the balls will be the same color?

Short Answer

Expert verified

answer=0.5.

Step by step solution

01

Given Information.

An urn Acontains 3red and3black balls, whereas the urn Bcontains 4red and6black balls and a ball is randomly selected from each urn.

02

Explanation.

There are 2cases:

Case1:

Both the balls are red. The probability that the ball chosen from the urn Ais red is 36and that the ball chosen from the urn Bis red is410. These events are independent. Therefore, the total probability is36*410.

Case 2:

Both the balls are black. The probability that the ball chosen from the urn Ais black is36and that the ball chosen from the urn Bis black is610. These events are independent. Therefore, the total probability is36*610.

The final probability is the sum of the probabilities in cases 1and2. Therefore,

answer=36*410+36*610=3060=0.5.

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