Respuesta :
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;
[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......[/tex]
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) = [tex]\binom{2}{2} \times 0.01^{2} \times (1-0.01)^{2-2}[/tex]
= [tex]1\times 0.01^{2} \times 0.99^{0}[/tex]
= 0.0001
Therefore, probability that both eggs are cracked is 0.0001.
