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Chapter 3: Q. 3.4 (page 109)

Urn Acontains 2white balls and 1black ball, whereas urn Bcontains1white ball and 5black balls. A ball is drawn at random from urn Aand placed in urn B. A ball is then drawn from urn B. It happens to be white. What is the probability that the ball transferred was white?

Short Answer

Expert verified

By Bayer's formula,the colour was trasfered to the ball atPWA鈭�WB=45.

Step by step solution

01

Step: 1 Events:

The white ball drawn from Urn A- WA

The white ball drawn from Urn B- WB

The number of balls from Ais

PWA=23PWAc=13

The ball transfers from Ato B,the conditional distribution of ball Bis

PWB鈭�WA=27PWB鈭�WAc=17

02

Step: 2 Finding values:

By Bayes formula,

PWA鈭�WB=PWB鈭�WAPWAPWB鈭�WAPWA+PWB鈭�WAcPWAcPWA鈭�WB=27脳2327脳23+17脳13PWA鈭�WB=45.

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