Example 1 For the random variables described below, which have binomial distribu

Question

Example 1

For the random variables described below, which have binomial distributions?

a) You toss a balanced coin 50 times and count the number of heads.

b) Replacement heart valves have a probability of 0.77 of performing well for 15 years. It is reasonable to assume that values in different patients fail (or not) independently of each other. Let X be the number of patients in a group of 500 who will need another valve replacement within 15 years.

c)You deal 10 cards from a shuffled deck and count the number of red cards.

Explanation / Answer

(a)

This will have a binomial distribution because the event of getting a head can be termed as a success and hence can be given a score of 1.

(b)

This will have a binomial distribution, because X denotes the number of failures amongst the group of 500, and the probability of failure is 1-0.77 = 0.23

(c)

This is not a binomial distribution , because the probability of getting a second red card is different from the first.

This means that independence is not there. So this case doesn't fit for a binomial distribution pattern.

Hope this helps !

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