Question

You are rolling the pair of dice over and over until the minimum of the two dice is greater than or equal to 5. What is the expected number of times you must roll the pair of dice before you stop?

Answer 1

9

Explanation:

we are rolling two die until we get minimum of 5 in two die

we get (5,5) (5,6) (6,5) (6,6)

total number of sample space =36 as two die is rolled

so the probability of the event
`p=(4)/(36)=(1)/(9)`

so
`p\left ( X=x \right )=(4)/(36)\left ( 1-(4)/(36) \right )^(x-1)`

where x=1,2,3,4--------------

`=\sum (1)/(9)* (1-(4)/(36))^(x-1)x`

`=(1)/(9)\left ( 1-\overline{1-(1)/(9)} \right )^(-2)=(36)/(4)=9`