MHT CET202123 Sep 2021Evening ShiftMathematicsProbabilityActual
The probability distribution of the number of doublets in four throws of a pair of dice is given by
Options
- Aarray |l|l|l|l|l|l| X : & 0 & 1 & 2 & 3 & 4 P ( X ): & 1 5 & 1 5 & 1 5 & 1 5 & 1 5 array
- Barray |l|l|l|l|l| X : & 0 & 1 & 2 & 3 P ( X ): & 1 4 & 1 4 & 1 4 & 1 4 array
- Carray |l|l|l|l|l|l| X : & 0 & 1 & 2 & 3 & 4 P ( X ): & 1 4 & 1 4 & 1 4 & 1 4 & 1 4 array
- Darray |l|l|l|l|l|l| X : & 0 & 1 & 2 & 3 & 4 P ( X ): & 625 1296 & 125 324 & 25 216 & 5 324 & 1 1296 array
Correct answer
D. array |l|l|l|l|l|l| X : & 0 & 1 & 2 & 3 & 4 P ( X ): & 625 1296 & 125 324 & 25 216 & 5 324 & 1 1296 array
Step-by-step solution
Let p = Probability of getting a doublet in a throw of pair of dice. p = 6 36 = 1 6 and q =1- 1 6 = 5 6 Dice are thrown 4 times. Let X =0,1,2,3,4 denote number of times a doublet is obtained. When X =0, p = 5 6 5 6 5 6 5 6 = 625 1296 When X =1, p = ( ^4 C ₁ ) 1 6 5 6 5 6 5 6 = 125 324 aligned & X=2, p= ( ^4 C₂ ) 1 6 1 6 5 6 5 6 = 25 216 & X=3, p= ( ^4 C₃ ) 1 6 1 6 1 6 5 6 = 5 324 & X=4, p= 1 6 1 6 1 6 1 6 = 1 1296 aligned