In 4 throws with a pair of dice , what is the probability of throwing doublets at least twice ?

Options

A. `(7)/(36)`
B. `(17)/(144)`
C. `(19)/(144)`
D. None of these

Answer

C

Explanation

In a single throw of a pair of dice we have
`n(S) =(6xx6) =36`
Let E={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}
Then P(E ) `=(n(E ))/(n(S)) =(6)/(36) =(1)/(6) P " (not E ) " =(1-(1)/(6)) =(5)/(6)`
`:. , p =(1)/(6),q =(5)/(6) ` and n=4
Required probability =P(2 or 3 ro 4 successes)
`=.^(4)C_(2).((1)/(6))^(2).((5)/(6))^(2)+.^(4)C_(3).((1)/(6))^(3).((5)/(6))+.^(4)C_(4).((1)/(6))^(4)`
`=((25)/(216)+(5)/(324)+(1)/(1296)) =(171)/(1296) =(19)/(144)`