Question

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of number of successes.

Answer 1

Total outcomes=36
Probability of success=P=6/36=1/6
Probability of failure=Q=30/36=5/6
X=no. of times we get a doublet
`P(x=0)=4C_0(1/6)^0(5/6)^4=625/1296`
`P(x=1)=4C_1(1/6)^1(5/6)^3=500/1296`
`P(x=2)=4C_2(1/6)^2(5/6)^2=150/1296`
`P(x=3)=4C_3(1/6)^3(5/6)^1=20/1296`
`P(x=4)=4C_4(1/6)^4(5/6)^0=1/1296`