In a cricket match, if the probability that Dhoni will make a century in any match is \(\rm \dfrac {4}{5}\), then what is the probability that he will make at least one century in three matches?

Concept:

• P(not E) = 1 - P(E).
• Probability of a Compound Event [(A and B) or (B and C)] is calculated as:
  P[(A and B) or (B and C)] = [P(A) × P(B)] + [P(C) × P(D)]    ('and' means '×' and 'or' means '+')

Calculation:

Probability of Dhoni making a century = \(\rm \dfrac {4}{5}\).

Probability of Dhoni not making a century = \(\rm 1-\dfrac {4}{5}=\dfrac {1}{5}\).

Probability of Dhoni making no century in three matches:

P(not century) AND P(not century) AND P(not century)

P(not century) × P(not century) × P(not century)

= \(\rm \dfrac {1}{5}\times \dfrac {1}{5}\times \dfrac {1}{5}= \dfrac {1}{125}\).