1. Two fair coins are tossed and the events A and B are defined as follows: A: {

Question

1.

Two fair coins are tossed and the events A and B are defined as follows:

A: {At least one head appears}

B: {Exactly one head appears}

Find P (A)

2.

Consider the following discrete probability distribution:

    x             -2     -1     0    1        2         

P(x)          0.10     0.08     0.23     0.31     0.28       

Calculate the mean (µ) of this discrete probability distribution.

3. Suppose that 10% of the Golden Retrievers in the U.S. have a particular genetic defect. We randomly select 6 Golden Retrievers from the population consisting of all Golden Retrievers in the U.S. What is the probability that at least one (i.e., one or more) of the 6 dogs in the sample will have the genetic defect? To find the answer to this question, you may use either the binomial equation or you may use the attached binomial probability table.

4. The American Journal of Public Health published a study of the relationship between passive smoking and nasal allergies in Japanese female students. The study revealed that 80% (i.e., p = 0.80) of the students from heavy-smoking families showed signs of nasal allergies on physical examinations. Consider a sample of 10 Japanese female students exposed daily to heavy smoking in their families. What is the probability that at least 7 (i.e., 7 or more) of the 10 students will have nasal allergies?

Explanation / Answer

As per the chegg policy, we are advised to attempt only one question at a time so i am attempting the 1st one.

1. The sample space will be: {HH, HT, TH, TT}

Where H represents Heads and T represents Tails.

So,

P(A)

= P(At least one head)

= 1 - P(No Head)

= 1 - 1/4

= 3/4

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