Question
A bag contains 'a' white and 'b' black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after the draw. A begins the game. If the probability of A winning ( that is
drawing a white ball) is twice the probability of B winning, then the ratio a : b is equal to
drawing a white ball) is twice the probability of B winning, then the ratio a : b is equal to
Answer: Option C
:
C
Let the event when a white ball is draw be W and for black ball let it be B. So A wins when we get sequence of the form
W or WBW or WBBBW or WBBBBBW......
Probability of getting W is a/a+b . So we get
P(A)=aa+b+(ba+b)2aa+b+(ba+b)4aa+b+...∞=a+ba+2bSimilarlywegetP(B)=ba+b.aa+b+(ba+b)3aa+b+...∞=ba+2bP(A)=2P(B)⇒a+b=2b⇒a=b.
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:
C
Let the event when a white ball is draw be W and for black ball let it be B. So A wins when we get sequence of the form
W or WBW or WBBBW or WBBBBBW......
Probability of getting W is a/a+b . So we get
P(A)=aa+b+(ba+b)2aa+b+(ba+b)4aa+b+...∞=a+ba+2bSimilarlywegetP(B)=ba+b.aa+b+(ba+b)3aa+b+...∞=ba+2bP(A)=2P(B)⇒a+b=2b⇒a=b.
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