134 CHAPTER 4/PROBABILITY (b) State the compositions of the events (b) The propo

Question

134 CHAPTER 4/PROBABILITY (b) State the compositions of the events (b) The proportion of cars that do not meet emission standards if the data are collected from service stations where the mechanics have been asked /. [ exactly one certificate is sent to the correct person ] to check emissions while attending to other B-[all of the certificates are sent to requested services. incorrect persons] 1.32 A local bookstore intended to award three gift certificates in the amounts $100, $50, and $25 to the 4.33 Refer to Exercise 4.32. first, second, and third customer to identify a mystery(a) Assign probabilities to the elementary outcomes author. Unfortunately, a careless clerk in charge of mailing forgot the order and just randomly placed the gift certificates in the already addressed envelopes. 4.34 Refer to Exercise 4.28. Using relative frequencies (a) List the sample space using F, S, and T for the to estimate probabilities, find whiçh 3 consecutive (b) Find P(A) and P(B) three persons. months have the lowest probability of a new birth.

Explanation / Answer

(a) the ways in which the letter can be sent =3! = 6 ways

Sample space = {FST, FTS, TSF, TFS, STF, SFT}

Where , FST is the order in which the letter can be sent.

(b)

A= Exactly one certificate is sent to the correct person.

So either F is correct and S and T are wrong, which can happen in only 1 way {FTS}

Or, S is correct and the other two is wrong. This can also happen in one way {TSF}

Or, T Is correct only. This can again happen in one way {SFT}.

Thus , A= {FTS, TSF, SFT}

B = all the letters are sent to the wrong person.

So, B={STF, TFS}

Since F can't be send first, it goes either second ot third.

Similarly, S and T can't go second and third respectively, so it goes third and second respectively.

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