Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6) and let `E_k={(a,b)in S:ab=k}` for `k >= 1` If `p_k=p(E_k)` for `k >= 1` then correct among the following, is (Eamcet 2008)

Options

A. `p_(1)lt p_(30)lt p_(4)lt p_(6)`
B. `p_(36)lt p_(6)lt p_(2)lt p_(4)`
C. `p_(1)lt p_(11)lt p_(4)lt p_(6)`
D. `p_(36)lt p_(11)lt p_(6)lt p_(4)`

Answer

A

Explanation

Given, `E_(k)={(a,b)in S : ab = k}` for `k ge 1` and `p_(k)=P (E_(k))`
Now, `E_(1)={(1,1)} rArr p_(1) =P(E_(1))rArr p_(1)=(1)/(36)`
`rArr E_(2)={(1,2),(2,1)} rArr p_(2) = P(E_(2)) rArr p_(2) =(2)/(36)`
`rArr E_(4)= {(1,4),(4,1),(2,2)} rArr p_(4) = P(E_(4)) rArr p_(4)=(3)/(36)`
`rArr E_(6)={(1,6),(6,1),(2,3),(3,2)}`
`rArr p_(6) = P (E_(6)) rArr p_(6)=(4)/(36)`
and `E_(30)={(5,6), (6,5)}`
`rArr p_(30)=P(E_(30)) rArr p_(30)=(2)/(36)`
`therefore` From the above results, we get `p_(1) lt p_(30)lt p_(4) lt p_(6)`