Tree diagrams can organize problems having more than two stages. The figure belo

Question

Tree diagrams can organize problems having more than two stages. The figure below shows probabilities for a charity calling potential donors by telephone. (The probabilities given are realistic, according to the fundraising firm SCM Associates, scmassoc.com.) Each person called is either a recent donor, a past donor, or a new prospect. At the next stage, the person called either does or does not pledge to contribute, with conditional probabilities that depend on the donor class the person belongs to. Finally, those who make a pledge either do or don't actually make a contribution.

(a) What percent of calls result in a contribution? (Use 1 decimal place.)

(b) What percent of those who contribute are recent donors? (Use 1 decimal place.)

Explanation / Answer

a. 0.5*0.4*0.8+0.3*0.3*0.6+0.2*0.1*0.5= 0.224 just multipiled the branch probabailties ending contribution through brach from initial point, and added in between because it could be first or second or third case coming there.i.e contribution can come from recent donor or past donor or new prospect

b. (0.5*0.4*0.8) /0.224 = 71.4%

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