Question

A bag contains 9 identical balls, of which are 4 are blue and 6 are green. Three balls are taken out randomly from the bag after one another. Find the probability that all three balls are blue?

(a) \(\frac {5}{8}\)

(b) \(\frac {6}{19}\)

(c) \(\frac {5}{21}\)

(d) \(\frac {4}{7}\)

The question was posed to me in examination.

I would like to ask this question from Multiplication Theorem on Probability in chapter Probability of Mathematics – Class 12

Answer 1

Right choice is (c) \(\frac {5}{21}\)

For explanation I would say: Since  6 balls are green, the probability of first ball to be drawn is green = \(\frac {6}{9}\)

The probability of the first ball to be green, 8 balls are left and 5 out of them are green = \(\frac {5}{8}\)

If the first two balls are green, then the probability of the third ball to be green = \(\frac {4}{7}\)

According to multiplication theorem, \(\frac {6}{9} . \frac {5}{8} . \frac {4}{7} = \frac {5}{21}\)