Question

The probability that an egg on a production line is cracked is 0.01. Two eggs are selected at random from the production line. Find the probability that exactly one of the eggs is cracked. Write the entire decimal answer.

Answer 1

Probability that exactly one of the eggs is cracked is 0.0198.

Explanation:

We are given that the probability that an egg on a production line is cracked is 0.01.

Two eggs are selected at random from the production line.

The above situation can be represented through binomial distribution;

`P(X = r) = \binom{n}{r} * p^(r) * (1-p)^(n-r);x=0,1,2,3,.......`

where, n = number trials (samples) taken = 2 eggs

r = number of success = exactly one

p = probability of success which in our question is probability that

an egg on a production line is cracked i.e; p = 0.01

Let X = Number of eggs on a production line that is cracked

So, X ~ Binom(n = 2, p = 0.01)

Now, probability that exactly one of the eggs is cracked is given by = P(X = 1)

P(X = 1) =
`\binom{2}{1} * 0.01^(1) * (1-0.01)^(2-1)`

=
`2 * 0.01 * (0.99)^(1)`

= 0.0198

Therefore, the probability that exactly one of the eggs is cracked is 0.0198.