1) Every night there is a 20% chance that Mrs. Lemonde will let Mr.Lemonde’s dog George...

1) Every night there is a 20% chance that Mrs. Lemonde will let Mr.Lemonde’s dog George sleep in the bed. Using binomial distributions answer the following:

a) What is the probability that George sleeps with Mr. Lemonde exactly twice in one week? Explain

b) What is the probability that George sleeps with Mr. Lemonde at least once in one week?

Solutions

Expert Solution

Every night there is a 20% chance that Mrs. Lemonade will let George sleep in the bed.

So, the probability that Mrs. Lemonade lets George sleep with her, on a randomly selected night, is 0.2.

And the chance that Mrs. Lemonade does not let George sleep with her, is (1-0.2), ie. 0.8.

Now, there are 7 nights in a week.

So, if X be the random variable, denoting the number of nights in a week when Mrs. Lemonade lets George sleep with her.

So, X follows binomial distribution, with parameters n=7, and p=0.2.

So, the probability mass function of X is

Where, i can take integer values from 0 to 7.

(a) We have to find the probability that George sleeps with Mrs. Lemonade twice in a week.

So, we have to find

So, the required probability is 0.2752.

(b) We have to find the probability that George sleeps with Mrs. Lemonade, at least once in a week.

So, we have to find

So, the required probability is 0.7903.

orchestra answered 1 year ago

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