MHT CET · Maths · Probability

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 $\frac{19}{2048}$
D $\frac{19}{4096}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{19}{4096}$

Step-by-step Solution

Detailed explanation

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}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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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 ________

Step-by-step Solution

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 ________