Question

Suppose that 9 good fuses and 4 defective ones have been mixed up. To find the defective fuses, we test them one-by-one, at random. What is the probability that we are lucky and find both of the defective fuses in the first two tests?

1). With replacement

2). Without replacement

Answer 1

1)

$$P(both\ defective)=\dfrac{4}{9+4}(\dfrac{4}{9+4})=\dfrac{16}{169}$$

2)

$$P(both\ defective)=\dfrac{4}{9+4}(\dfrac{4-1}{9+4-1})=\dfrac{1}{13}$$