Q57 / 150 · MHT CET 2019 (02 May Shift 1) · Mathematics

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 ________

A
${(\frac{1}{4})}^{6}$
B
$\frac{19}{1024}$
C
$\frac{19}{2048}$
Correct answer
D
$\frac{19}{4096}$

Solution

P = \frac{1}{4} q = \frac{3}{4} n = 6

Required Probability

= P (x = 5) + P (x = 6)

=^{6} C_{5} {(\frac{1}{4})}^{5} \frac{3}{4} + {(\frac{1}{4})}^{6}

∵ (p (x = r)) =^{n} C_{r} p^{r} q^{n - r}

= \frac{19}{4096}

Hence, the correct answer is option: 'D'.

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