JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Probability

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is

\frac{1}{4}

. If the probability that at most two machines will be out of service on the same day is

(\frac{3}{4})^{3} k

, then k is equal to:

Answer: (B)

Solution

With

n = 5

p = \frac{1}{4}

and

q = \frac{3}{4}

, the chance that at most two machines are out is

P (X \leq 2) = (0 5) q^{5} + (1 5) p q^{4} + (2 5) p^{2} q^{3}

. Pulling out

(\frac{3}{4})^{3}

leaves

(\frac{3}{4})^{3} [\frac{9}{16} + \frac{15}{16} + \frac{10}{16}] = (\frac{3}{4})^{3} \cdot \frac{34}{16} = (\frac{3}{4})^{3} \cdot \frac{17}{8}

, so

k = \frac{17}{8}

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Single correct option