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in Binomial Distribution by (25.9k points)
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A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of 

(i) 5 successes 

(ii) at least 5 successes 

(iii) at most 5 successes.

1 Answer

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Best answer

Let X = number of successes, i.e. number of odd numbers. 

p = probability of getting an odd number in a single throw of a die

The p.m.f. of X is given by

Hence, the probability of 5 successes is 3/32.

(ii) P(at least 5 successes) = P[X ≥ 5] 

= p(5) + p(6)

Hence, the probability of at least 5 successes is 7/64.

(iii) P(at most 5 successes) = P[X ≤ 5] = 1 – P[X > 5]

Hence, the probability of at most 5 successes is 63/64.

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