Q68 / 150 · MHT CET 2019 (Shift 1) · Mathematics

Let X be the number of successes in ‘n’ independent Bernoulli trials with probability of success $p = \frac{3}{4}$ . The least value of ‘n’ so that $P (X \geq 1) \geq 0.9375$ is….

Correct answer
A
2
B
1
C
4
D
3

Solution

We have,

p = \frac{3}{4}, q = 1 - p = \frac{1}{4}

It is given that

P (X \geq 1) \geq 0.9375

= 1 - P (X = 0) \geq 0.9375

= 1 -^{n} C_{0} (p^{0}) {(g)}^{n - 0} \geq 0.9375

= 1 - {(\frac{1}{4})}^{n} \geq 0.9375

= 1 - 0.9375 \geq {(\frac{1}{4})}^{n}

= 0.0625 \geq {(\frac{1}{4})}^{n}

= \frac{625}{10000} \geq {(\frac{1}{4})}^{n}

= \frac{1}{16} \geq {(\frac{1}{4})}^{n}

= 16 \leq 4^{n}

\Rightarrow n = 2

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

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