Question

A batch of 50 parts contains six defects. If two parts are drawn randomly one at a time without replacement, what is the probability that both parts are defective?

Answer 1

we know that

P(both parts defective) = P(1st is defective) * P(2nd is defective)  

Probability of 1st detective:

total parts =50

number of defects =6

so,

P(1st is defective)

$=\frac{6}{50}$

Probability of 2nd detective:

total parts =49

number of defects =5

so,

P(2nd is defective)

$=\frac{5}{49}$

Probability of both detective:

P(both parts defective) is

$=\frac{6}{50} *\frac{5}{49}$

$=\frac{3}{245}$...............Answer