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g south univerity campur x YD Qaanturive Analysis C Secure https/ aspahomeworkld-42s587655&questionld; 24nushed tale&cld; 44so3618back DoAssignments.aspw Quanttative Aalysis Decision Making IMBAS006 501 (A) Homework: W2 Assignment 1 Homework Score: 0 2 pts 5 or 150 complete) 3.3.39 HW Score: 10 48%, 314 of 30 pts A local public acton solces doratons Forapascularistofprospects Question Help a request for further information by telephone was estimated that for individual heprtabity was 005 of an immedate donation by credt card, 025 of no immediate dona on tut mough the mal, 70of What is estimated of these people wil eventually donate An operator makes b What is the probability the first calleading to an immedale credit tad donaton isprecede atleast a The probablry that the trstcal leading to any donation feither immediately eventually anera malinglispreceded by at least six cals never lead to a probably that no ammediate credit card donation wil be received intl at least six calls where no immedale donations awe made is your answer in the answer box and then chek Check Answer

Explanation / Answer

a) P(immediate donation) = 0.05

P(no immediate donation) = 1 - 0.05 = 0.95

We have to calculate the probability that the first call that leads to an immediate donation is preceded by atleast six calls that don't. This means that the first immediate donation call should occur from the 7th call onwards. To calculate this probability we can calculate the reverse (immediate donation on the 1-6th call) probability and subtract from 1:

P(1st immediate donation >= 7th call) = 1 - P(1st immediate donation < 7th call)

Thus,

P(1st immediate donation < 7th call) = P(immediate donation = 1st call) + P(immediate donation = 2nd call) +.....+ P(immediate donation = 6th call)

=> 0.05 + 0.95*0.05 + 0.05*0.952 + 0.05*0.953 +0.05*0.954 +0.05*0.955 = 0.265

Thus,

P(1st immediate donation >= 7th call) = 1 - 0.265 = 0.735

b) Donation occurs in 2 ways: immediate (0.05) or after the e-mail (35% of 0.25)

Thus,

P(donation) = 0.05 + 0.35*0.25 = 0.1375

P(no donation) = 0.8625

Now the procedure for this part is the same as the first part. We will calculate the probability that a donation occurs in the first 6 calls and subtract it from 1 to get the answer:

P(donation in first 6 calls) = 0.1375(1 + 0.8625 + 0.86252 + 0.86253 +0.86254 +0.86255) = 0.588

Thus,

P(1st donation >= 7 calls) = 1 - 0.588 = 0.412

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