Question

The probability that an egg on a production line is cracked is 0.01. Two eggs are selected at random

Answer 1

Answer:

Probability that both eggs are cracked is 0.0001.

Step-by-step 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;

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

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) =  $\binom{2}{2} \times 0.01^{2} \times (1-0.01)^{2-2}$

                              =   $1\times 0.01^{2} \times 0.99^{0}$

                              =  0.0001

Therefore, probability that both eggs are cracked is 0.0001.