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Question

The odds in favour of A solving a problem are 3 to 4 and the odds  against B solving the same problem are 5 to 7.  If they  both try the problem, the probability that the problem is solved is:
  1. 4184
  2. 1621
  3. 521
  4. 14


Solution

The correct option is B 1621
P(A)=37,P(B)=712P(¯A)=47,P(¯B)=512P(AB)=1P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB)=1P(¯A¯B)P(AB)=147×512=1621

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