Two natural numbers are chosen at random from 1 to 100 and are multiplied. If A is the event that the product is an even number and B is the event that the product is divisible by 4 , then P(A B )=

Step-by-step solution

Total number of pairs from 1 to 100= ¹⁰⁰ C ₂n( ~A )= Total number of pair whose product is even = 50 _ array c one odds one even array C ₁ ⁵⁰ C ₁+ ⁵⁰ C ₂ _ array c both even array n(B)= Total number of pair whose product is divisible by 4 aligned & 5^0 C ₂ _ array c both are even array + n( ~A ~B )= ⁵⁰ C ₂+ ⁵⁰ C ₁ 25 _ array c one odd & one 4,8,12 100 50 C ₁ 25 array aligned Required probability = ⁵⁰ C ₁ ⁵⁰ C ₁+ ⁵⁰ C ₂- ⁵⁰ C ₂- ⁵⁰ C ₁+25 ¹⁰⁰ C ₂ = 25 99