One machine produces 25 pieces, 2% defective. What is the probability that there are at least 2 defectives?

Question

The exercise:

A machine produces certain parts that are packaged in batches of 25 units. Usually produces 2% of defective parts.

Calculate the probability that there are two or more defective parts in a batch.

What I thought:

The $2$% of $25$ is $0.5$, then it produces $0.5 / 25 = 1/50 = p$ defective parts, and finally $25 = n$ parts must be analyzed for the probability of obtaining $X : "Number$ $of$ $defective$ $parts"$.

$P(X\geqslant2)=1-P(X<2)=1-P(X\leqslant 1) = 1-F_X(1)$

My doubts:

• This is a $X$~$Bin(25,1/50)$?
• The answer is $1-F_X(1)$?

Answer 1

Probability for no defectives is $(0.98)^{25}$

Probability for exact 1 defective piece is $\dbinom{25}{1}(0.02)^{1}(0.98)^{24}$

So, required probability is

$1-(0.98)^{25}-\dbinom{25}{1}(0.02)^{1}(0.98)^{24}$