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Chapter 3: Q.3.38 (page 100)

Urn Ahas 5white and 7black balls. Urn Bhas 3white and 12black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?

Short Answer

Expert verified

The probability that the coin landed tails is 1237.

Step by step solution

01

Given information

Urn Ahas 5white and 7black balls. Urn Bhas 3white and 12black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected.

02

Solution

Urn A5 white

7Black⇒P(white)=512

Urn B3 White

12Black⇒P(white)=315

P(Tail | white)=12×31512×315+12×512

=330×24074

=1237

03

Final answer

The probability that the coin landed tails is1237.

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