1. With replacement 2. Without replacement please help

Question

1. 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? (5 points) 

1). With replacement 

2). Without replacement

Answer 1

4+9 = 13 total fuses

4 defective, 9 not

mix them up, test the one by one

probability first test will find a defective is 4/13

without replacement, 2nd will find another defective with probability = 3/12.

probability of finding 2 defectives on 1st two tests is

4/13 x 3/12 = 12/156= 1/13

with replacement the probability is 4/13 x 3/13 = 12/169