A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to…

A lot of 100 bulbs contains 10 defective bulbs. Five bulbs selected at random from the lot and sent to retail store, then the probability that the store will receive at most one defective bulb is
  1. 0.59049
  2. 0.91854
  3. 0.6561
  4. 0.32805

Solution

Probability of finding defective bulb $=\frac{10}{100}=0.1$ Let $\mathrm{p}=0.1 \Rightarrow 1=0.9$ We have $\mathrm{n}=5$ and to get required probability $\mathrm{x}=0$ and $\mathrm{x}=1$ $\begin{aligned} & \therefore \mathrm{P}={ }^5 \mathrm{C}_0(0.1)^2(0.9)^5+{ }^5 \mathrm{C}_1(0.1)^1(0.9)^4 \\ & (0.9)^5+(5)(0.1)(0.9)^4 \\ & =(0.9)^4[0.9+0.5]=(0.9)_4(1.4) \\ & =(0.81)(0.81)(1.4)=(0.6561)(1.4)=0.91854 \end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 1)

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