Question

A box contains 100 balls numbers from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd ? 

(a) \(\frac{3}{8}\)

(b) \(\frac{1}{2}\)

(c) \(\frac{3}{4}\)

(d) \(\frac{1}{4}\)

Answer 1

(d) \(\frac{1}{4}\)

The box contains 100 balls numbered from 1 to 100. Therefore, there are 50 even and 50 odd numbered balls. The sum of the three numbers drawn will be odd, if all three are odd or one is even and 2 are odd. 

∴ Required probability = P(odd) × P(odd) × P(odd) + P(even) × P(odd) × P(odd)