Question

A bag contains 4 red balls and 5 blue balls. Two balls are drawn at random without replacement. If the first ball drawn is blue, what is the probability the second ball is also blue?

1. \(\frac 5 9\)
2. \(\frac 1 2\)
3. \(\frac {5}{18}\)
4. \(\frac 4 9\)

Answer 1

Correct Answer - Option 2 : \(\frac 1 2\)

Concept:

If S is a sample space and A is a favourable event then the probability of A is given by:

\(\rm P(E)=\dfrac{n(A)}{n(S)}\)

 

Calculation:

Total balls in bag = 4 + 5 = 9 balls

Given: Two balls are drawn at random without replacement

After the first ball is drawn and found to be blue, there are now 8 balls left in the bag, 4 of which are blue.

Probability the second ball is blue = \(\frac 4 8 = \frac 1 2\)