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 at least one egg is cracked. Write the entire decimal answer.

Answer 1

`P(X \geq 1)=1-P(X<1)= 1- P(X=0)`

`P(X=0)=(2C0)(0.01)^0 (1-0.01)^(2-0)=0.9801`

And replacing we got:

`P(X \geq 1) = 1-0.9801 = 0.0199`

Explanation:

Let X the random variable of interest "number of craked eggs", on this case we now that:

`X \sim Binom(n=2, p=0.01)`

The probability mass function for the Binomial distribution is given as:

`P(X)=(nCx)(p)^x (1-p)^(n-x)`

Where (nCx) means combinatory and it's given by this formula:

`nCx=(n!)/((n-x)! x!)`

And we want to find this probability:

`P(x \geq 1)=1-P(X<1)= 1- P(X=0)`

And we can find the probability:

`P(X=0)=(2C0)(0.01)^0 (1-0.01)^(2-0)=0.9801`

And replacing we got:

`P(X \geq 1) = 1-0.9801 = 0.0199`