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Question

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting equal numbers on the dice is
  1. 0.2
  2. 0.1
  3. 0.5
  4. 0.25


Solution

The correct option is A 0.2

Let us define the eventsA: getting equal numbers on dice.B: the sum of the numbers is less than 6.Then we have to find P(A|B).Sample space, S=((x, y): x, y=1, 2, 3, 4, 5, 6}.Thus, n(S)=36A=((1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}B=((x, y): x+y<6}i.e., B=((1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}i.e., n(B)=10Clearly, AB=((1, 1), (2, 2)}Now, P(B)=1036 and P(AB)=236Then P(A|B)=P(AB)P(B)     P(A|B)=2361036     P(A|B)=210=0.2               




 

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