Question

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

विकल्प

• `(1/4)^6`

• `19/1024`

• `19/2048`

• `19/4096`

Answer 1

It is observed that 25% of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the probability that atleast 5 of them will be solved is `underline(19/4096)`.

Explanation:

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 stations are solved.

∴ According to question,

P(X = 5) + P(X = 6)

`= "^6C_5 (p)^5 (q)^(6-5) + ^6C_6 (p)^6 (q)^(6 - 6)`

`= "^6C_1 (1/4)^5 (3/4)^1 + ^6C_0 (1/4)^6 (3/4)^0`

`= 1/(4)^6 [6 xx 3 + 1]`

`= 19/4096`