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Question

Family A has 6 members of which 4 are males and 2 are females & family B has 5 members of both genders. (Assume it is equi-probable for a member of unknown gender to be a male or female).
Probability that family B has more females than males is equal to

  1. 34
  2. 12
  3. 23
  4. 13

A
34
B
12
C
13
D
23
Solution
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Family A has 6 mambers :4 males and 2 females.
Family B has 5 members :
Let the probability of family B having females be 12
In Family A, 6C4×6C2=225
In Family B, given that no. of females greater than males, females be 3 and males be 2 or females be 4 and males be 1
5C3×5C2=100 and 5C4×5C1=25
So, in Family B =25100×2=24=12.
Hence, the answer is 12.

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