Consider the following events: `E_(1)`: Six fair dices are rolled and at least one die shows six. `E_(2)`: Twelve fair dice are rolled and at least two dice show six. Let `p_(1)` be the probability of `E_(1)` and `p_(2)` be the probaility of `E_(2)`. Which of the following is true? (A) p1 > p2 (B) p1 = p2 = 0.6651 (C) p1 < p2 (D) p1 = p2 = 0.3349

Options

A. `p_(1) gt p_(2)`
B. `p_(1)=p_(2)=0.06651`
C. `p_(1) lt p_(2)`
D. `p_(1)-p_(2)=0.3349`

Answer

A

Explanation

`p_(1)`=1-(no die show six )
`1-(((5)/(6))^(6))=0.6651`
`p_(2)=1-` ( no die shown two + one die shown two )
`p_(2)=1-[((5)/(6))^(12)+""^(12)C_(1)((5)/(6))^(11)((1)/(6))^(1)]=0.61866`
`p_(1) gt p_(2)`