Algebra

Probability

Medium

applied

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is: [Given $e^{-2}=0.135$ ]

0.5

0.135

0.27

✅ Correct Option: 4

The Poisson distribution is used for counting rare events, making it suitable for defect-type problems.

Given information:

2% of bolts are defective
Sample size: 100 bolts
Required: probability of exactly 2 defective bolts

The parameter $\lambda$ represents the expected number of defects.

$\lambda = \text{Total bolts} \times \text{Defect rate}$

$\lambda = 100 \times 0.02$

$\lambda = 2$

The Poisson formula:

$P(X = k) = \frac{\lambda^k \times e^{-\lambda}}{k!}$

where:

$k = 2$ (exactly 2 defective bolts)
$\lambda = 2$
$e^{-2} = 0.135$ (given)

For exactly 2 defective bolts:

$P(X = 2) = \frac{2^2 \times e^{-2}}{2!}$

$P(X = 2) = \frac{4 \times 0.135}{2}$

$P(X = 2) = \frac{0.54}{2}$

$P(X = 2) = 0.27$

Therefore, the probability is 0.27.

2026: 21 May Shift 1

If $P(A \cap B) = \frac{1}{2}$ , $P(A' \cap B') = \frac{1}{3}$ , $P(A) = p$ and $P(B) = 2p$ , then value of $p$ is

2025: 27 May Shift 1

For independent events $A_1, A_2, A_3, ..., A_n$ if $P(A_i) = \frac{1}{i+1}$ , $i = 1, 2, 3, ..., n$ , then the probability that none of the events occur is:

2025: 30 May Shift 1

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	k	2k	3k

If k > 0, then $P(0 < X \leq 2)$ is equal to

2025: 26 May Shift 2

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

2025: 2 June Shift 1

If the sum and difference of squares of mean and variance of a Binomial distribution is $\frac{225}{256}$ and $\frac{63}{256}$ respectively, the $P(X \geq 2)$ is:

2026: 14 May Shift 2

Four cards are drawn successively without replacement from a deck of 52 playing cards. The probability that all the four cards are king is:

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is: [Given e−2=0.135e^{-2}=0.135e−2=0.135]

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is: [Given $e^{-2}=0.135$ ]