A dice is thrown 6 times. If 'getting an old number' is a success, then match the terms of column I with their respective values in column II and choose the correct option from the codes given below.

Options

A. `{:(A,B,C),(1,2,3):}`
B. `{:(A,B,C),(3,1,2):}`
C. `{:(A,B,C),(1,3,2):}`
D. `{:(A,B,C),(3,2,1):}`

Answer

D

Explanation

The repeated tosses of a dice are Bernoulli trails . Let X denotes the number of successes i.e. , getting odd numbers, in an expriment of 6 trials .
p=P(success)
=P (getting an odd number in a single throw of a dice )
`p=(3)/(6)=(1)/(2)`
`therefore q=p` (failure) `=1-p=1-(1)/(2)=(1)/(2)`
Therefore, by binomial distribution
`P(X-r)=""^(n)C_(r) p^(r)q^(n-r), ` where r=0,1,2,...,n
`P=(X=r)=""^(6)C_(5)*((1)/(2))^(r)((1)/(6))^(6-r)=""^(6)C_(r)((1)/(2))^(6)`
A. P (5 successes) `=""^(6)C_(5)p^(5)q^(1)=""^(6)C_(1)((1)/(2))^(5)((1)/(2))`
`=(6)/(2^(6))=(6)/(64)=(3)/(32)`
B. P (atleast 5 successes)
`P(5 "successes")+ P (6 "sucsesses")`
`=""^(6)C_(5)p^(5)q^(1)+""^(6)C_(6)p^(6)q^(0)`
`=6xx((1)/(2))^(5)((1)/(2))^(1)+1* ((1)/(2))^(6)=(6)/(24)+(1)/(64)=(7)/(64)`
C. P (atmost 5 successes)=1-P(6 successes)
`=1-""^(6)C_(6)p^(6)q^(0)=1-1((1)/(2))^(6)`
`=(64-1)/(64)=(63)/(64)`