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A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8 , and B wins if he throws a sum of 8 before A throws a sum of 5 . The probability, that A wins if A makes the first throw, is

Options

  1. A8 17
  2. B9 19
  3. C9 17
  4. D8 19

Correct answer

B. 9 19

Step-by-step solution

For sum ' 5 ' (1,4),(2,3),(3,2)(4,1) P(A)= 4 36 For sum ' 8 ' (2,6),(3,5),(4,4) For sum ' 5 ' (1,4),(2,3),(3,2)(4,1) P(A)= 4 36 For sum ' 8 ' (2,6),(3,5),(4,4) aligned & (5,3),(6,2) P(B)= 5 36 & aligned P( A )= 32 36 & , P( B )= 31 36 aligned & aligned P(A wins )= & P(A)+P( A ) P( B ) P(A)+ & +P( A ) P( B ) P( A ) P( B ) P(A)+ = & P(A) 1-P( A ) P( B ) = 9 19 aligned aligned

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