See attached questions

Question

5.2/6 The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 20% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of six adult friends, what is the probability of the following? (Round your answers to three decimal places.)

(a) no one has done a one-time fling

 

(b) at least one person has done a one-time fling

(c) no more than two people have done a one-time fling

5.2 7) Sociologists say that 90% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that eleven married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.)

(a) All of them dislike their mother-in-law.

(b) None of them dislike their mother-in-law.

(c) At least nine of them dislike their mother-in-law.

(d) No more than eight of them dislike their mother-in-law.

9)A research team conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 15 businessmen, all of whom wear ties, what are the following probabilities? (Round your answers to three decimal places.)

(a) at least one tie is too tight

(b) more than two ties are too tight

(c) no tie is too tight

(d) at least 13 ties are not too tight

Answer 1

These are all questions about the Binomial Distribution, where there are exactly two possible outcomes for the events under consideration.

We need to use the probability fact that P(A) = 1 - P(A-complement)

and P(X = k) where X is the number of "successes" in n trials where probability of success is p

is given by nCk p^k ((1-p)^(n-k) Here nCk is number of combinations of n objects taken k at a time.

5.2/6 p = .20, n = 6

a) k = 0,

We want P(X = 0)

which is 6C0 .20^0 .80^6 = 1 * .80^6 = .2621 (rounded to 3 decimal places is .262)

The remaining problems 5.6/3 and are

b) P(At least 1 person has done a one-time fling)

= 1 - P(no people have done a one-time fling) = 1 - P(X = 0)

= 1 - .2621 = .7379 (rounded to 3 decimal places is .738)

c) P(No more than 2 people have done a one-fling) =

1 - P(0 people have done a one-time fling OR 1 person has done a one-time fling OR 2 people have done a one-time fling)

Since these events are disjoint, this is the same as

1 - [ P(0 people have done a one-time fling) + P( 1 person has done a one-time fling) + P( 2 people have done a one-time fling)]

We have calculated P(0 people have done a one-time fling) = .2621 in part a)

Now, P( 1 person has done a one-time fling) = 6C1 .2^1 .8^5 = 6 * .2^1 * .8^5 = .3932

and P( 2 people have done a one-time fling) = 6C2 .2^2 .8^4 = 15 * .2^2 * .8^4 = .2452

So, the desired probability is 1 - [.2621 + .3932 + .2452] = 1 - .9005 = .0995 (rounded to 3 decimal places is .100)

The remaining problems 5.2/7 and 9 are done similarly.