MHT CET202312 May 2023Morning ShiftMathematicsProbabilityActual
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then the probability distribution of number of jacks is
Options
- Aarray |l|c|c|c| X =x & 0 & 1 & 2 P ( X =x) & 144 169 & 24 169 & 1 169 array
- Barray |l|c|c|c| X =x & 0 & 1 & 2 P ( X =x) & 1 169 & 144 169 & 24 169 array
- Carray |l|c|c|c| X =x & 0 & 1 & 2 P ( X =x) & 24 169 & 1 169 & 144 169 array
- Darray |c|c|c|c| X =x & 0 & 1 & 2 P ( X =x) & 144 169 & 1 169 & 24 169 array
Correct answer
A. array |l|c|c|c| X =x & 0 & 1 & 2 P ( X =x) & 144 169 & 24 169 & 1 169 array
Step-by-step solution
Let X denotes the number of jacks Possible values of X are 0,1,2 P ( X =0)= ⁴⁸ C ₁ ⁴⁸ C ₁ ⁵² C ₁ ⁵² C ₁ = 144 169 aligned & P ( X =1)= ⁴⁸ C ₁ ^4 C ₁ ⁵² C ₁ ⁵² C ₁ + ^4 C ₁ ⁵² C ₁ ⁵² C ₁ ⁵² C ₁ = 24 169 & P ( X =2)= ^4 C ₁ ^4 C ₁ ⁵² C ₁ ⁵² C ₁ = 1 169 aligned Option (A) is correct.