Question

There are 10 rolls of film in a box and 3 are defective. Two rolls are to be selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?

Answer 1

Answer:   $\dfrac{1}{15}$

Step-by-step explanation:

Given : Total rolls of film in the box = 10

Defective rolls =3

Probability of selecting first defective roll = $\dfrac{\text{Number of bad rolls}}{\text{Total rolls}}$

$=\dfrac{3}{10}$

Now , total rolls left = 9

Total defective rolls left = 2

Probability of selecting second defective roll = $\dfrac{\text{Number of bad rolls}}{\text{Total rolls}}$

$=\dfrac{2}{9}$

Now , the probability of selecting a defective roll followed by another defective roll = $\dfrac{3}{10}\times\dfrac{2}{9}=\dfrac{1}{15}$

Hence, the probability of selecting a defective roll followed by another defective roll is $\dfrac{1}{15}$ .