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It is observed that 25% of the cases rel...

It is observed that 25% of the cases related to child labour reported to the polic station are solved. If 6 new cases are reported, then the probability that atleast 5 of them will be solved is

A

`(1/4)^(6)`

B

19/1024

C

19/2048

D

19/4096

Text Solution

Verified by Experts

The correct Answer is:
D
Here, n=6
`p=25%=1/4,q=1-p=3//4`
Let X be the random variable, which denotes the number of cases that police station are solved.
`therefore` According to question,
`P(X=5)+P(X=6)`
`=""^(6)C_(5)(p)^(5)(q)^(6-5)+""^(6)C_(6)(p)^(6)(q)^(6-6)`
`=""^(6)C_(1)(1/4)^(5)(3/4)^(1)+""^(6)C_(0)(1/4)^(6)(3/4)^(0)`
`=1/((4)^(6))[6xx3+1]=19/4096`
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