Worksheet- \"Calculating Probabilities from a Table\" ml65 Businesses that offer

Question

Worksheet- "Calculating Probabilities from a Table" ml65 Businesses that offer credit to their customers are inevitably faced with the task of collecting unpaid bills. An individual decided to study the collection remedies used by creditors. Part of this study involved asking a random sample of creditors in four states about how they deal with past due bills; the responses are tallied in the table below. "Tough actions" included filing a legal action, turning debt over to a third party such as an attorney or collection agency, garnishing wages, and repossessing property. 1. STATE W: Wisconsin M: Michigan A: Arkansas G: Georgia E: tough early L: tough late N: never tough a. For each of the following, find the value of the requested probability. 37 23 21 15 Each time ONE creditor is being selected randomly. P(A)22 P(A and N)- 6.399 P(M and A)6 P(A and G)- O P(W or A)52 P(L or )92 b. Describe (using words only) the probabilities found in part a. c. Describe (using words only) a pair of mutually exclusive events for this problem d. Explain in detail why your pair of events in part c is mutually exclusive.

Explanation / Answer

(a) P(N) = 41/151 = 0.2715

P(W or A) = P(W) + P(A) - P( W and A) = (46 + 33 - 0)/151 = 79/151 = 0.5232

P(L or G) = P(L) + P(G) - P(L and G) = (103 + 37 - 21)/151 = 119/151 = 0.7881

P(Ec) = 1 - P(E) = 1 - (7/151) = 144/151 = 0.9536

P(A) = 33/151 = 0.2185

P(A and N) = 6/151 = 0.0397

P(M and A) = 0/151 = 0

P(A and G) = 0/151 = 0

(b) P(N) = Is the probability that a state has a never tough action policy on a creditor.

P(W or A) = Is the probability that an action is taken on a creditor either in Wisconcin or Arkansas.

P(L or G) = Is the probability that an action taken on a creitor is tough late or an action is taken on a creditor in Georgia.

P(Ec) = Is the probability that ona creditor a tough early action is not taken.

P(A) = Is the probability of an action taken on a creditor in the state of Arkansas.

P(A and N) = Is the probability of a never tough action on a creditor in the state of Arkansas.

P(M and A) = 0/151 = Is the probability of the same action happening to a creditor in the states of Michigan and Arkansas.

P(A and G) = 0/151 = 0. Is the probability of the same action happening to a creditor in the states of Georgia and Arkansas.

(c) The event M and A are mutually exclusive. Similarly Events A and G are also mutually exclusive.

(d) These events are mutually exclusive as they cant occur at the same time. The common value is 0.A creditor in Michigan is not a creditor in georgia or arkansas, and hence the events are mutually exclusive.

W M A G Total E 0 1 5 1 7 L 37 23 22 21 103 N 9 11 6 15 41 Total 46 35 33 37 151

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