1. ## Probability

Question

5% of all batteries produced are defective. Batteries are sold in packs of 4.

1)What is the probability that a pack contains exactly 2 defective batteries?
2)Atleast 1 is defective?

My working

P (def) = 0.05 P (not def) = 0.95

P (2def) = 0.05 x 0.05 = 0.0025 *wrong

Alternative route > (5/100) x (4/99) = 0.00202 *wrong

2. You're dealing with binomial distribution $X \sim {\cal B}(n, p)$ where n=4, and p=0.05.

So you have to find $P(X=2)$ with $P(X=k)=\left({n \atop k}\right) p^k(1-p)^{n-k}$

At least one defective case can be found using probability of the complement
$P(X\geq 1)=1-P(X=0).$

3. Thanks MathoMan.. You are right.

I looked up Binomial Probability Distribution Function and it does correspond to what you have shown above.

Regards,

Bob