Question

the probability that a batsman scores a century in a cricket match is 1/3. what is the probability that in 4 matches he will score centuries in at least 3 innings?​

Answer 1

Answer:

Probability that Sachin scores a century is 0.4.

In four matches, the probability that he scores at least 3 centuries is given by

(Let X denote the number of centuries scored by him)

P(X=3)+P(X=4)

(43)×(0.4)3×(0.6)+

(44)(0.4)4≈17

Not good enough. Let's try it with 5 matches.

The probability that he scores at least 3 centuries in five matches is the sum of the probabilities of him scoring three, four or five centuries.

P(X=3)+P(X=4)+P(X=5)

(53)×(0.4)3×(0.6)2+

(54)×(0.4)4×(0.6)+

(55)(0.4)5≈31

So the answer is 5.