Question

A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one with replacement. What is the probability that all the 3 drawn are black if the first marbel is red?

Answer 1

The no . of red balls $5$

The no.of black balls $3$

The total no. of balls $5+3=8$

The probability of picking black ball in one event:

No.of favourable cases $3$

No. of possible cases $8$

Probability is given by $\frac{3}{8}$

The $3$ cases are independent so

The probability is given by ${\left(\frac{3}{8}\right)}^3$