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 0.3 Pladge check Not donor 05 0.6 0.3 No chack Noe 0.5 Pladge check Noe (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)

Just multiply and add all the positives:

So,

Total % = 0.5 * 0.4 * 0.8 + 0.3 * 0.3 * 0.6 + 0.2 * 0.1 * 0.5 = 0.224 or 22.4%

b) % who are recent donors and lead to contribution:

(.5 * .4 * .8)/.224 = 0.714 or 71.4%

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