Questions
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 till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, the ratio a:b is
detailed solution
Correct option is C
Let W denote the event of drawing a white ball at any draw and B that for a black ball. ThenP(W)=aa+b and P(B)=ba+bP(A wins the game)=P(W or BBW or BBBBW or …)=P(W)+P(BBW)+P(BBBBW)+⋯=P(W)+P(B)P(B)P(W)+P(B)P(B)P(B)P(B)P(W)+⋯=P(W)+P(W)P(B)2+P(W)P(B)4+⋯=P(W)1−P(B)2=a(a+b)a2+2ab=a+ba+2b Also P(B wins the game )=1−a+ba+2b=aa+2bAccording to the given condition,a+ba+2b=3ba+2b⇒a=2b⇒a:b=2:1Similar Questions
The odd against an event are 5 to 2 and the odds in favour of another disjoint event are 3 to 5. Then the probability that atleast one of the events will happen is
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