Three children took part in racing competition in their school with their respective probabilities to reach the finishing point being \(\frac{1}{6}\), \(\frac{1}{2}\) and \(\frac{1}{5}\) respectively. What is the probability that at least one of them will finish the race?

\(\frac{2}{3}\)

Let the names of children be x, y and z.

The probabilities of the three children to finish the race are \(\frac{1}{6}\), \(\frac{1}{2}\) and \(\frac{1}{5}\) respectively. It may be noted that one reaching the finishing point is independent of other reaching.

If P(x), P(y) and P(z) denotes the probabilities.

The probability of at least one of them reaching the finishing point

= 1 – P (none of them finishing the race)

= 1 – (\(\frac{5}{6}\) ) (\(\frac{1}{2}\)) ( \(\frac{4}{5}\)) = \(\frac{2}{3}\)

Hence, option B is correct.