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 both eggs are cracked. Write the entire decimal
answer.

Answer 1

Probability that both eggs are cracked is 0.0001.

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 = both eggs are cracked

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 are cracked

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

Now, Probability that both eggs are cracked is given by = P(X = 2)

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

=
`1* 0.01^(2) * 0.99^(0)`

= 0.0001

Therefore, probability that both eggs are cracked is 0.0001.