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Chapter 4: Problem 122

The probability that a corporation makes charitable contributions is .72. Two corporations are selected at random, and it is noted whether or not they make charitable contributions. a. Draw a tree diagram for this experiment. b. Find the probability that at most one corporation makes charitable contributions.

Short Answer

Expert verified
The probability that at most one corporation makes charitable contributions is .416

Step by step solution

01

Understand and Draw the Tree Diagram

A tree diagram is useful for visualizing and solving probability problems, in this case, whether a corporation makes charitable contributions or not. Since there are 2 corporations being selected with the probability of a charitable contribution being .72, we have four outcomes: Both Corporations donate (DD), First Corporation donates and Second does not (DN), First Corporation does not donate while Second does (ND), neither Corporation does (NN). The first branch from the root of the tree will represent the outcomes of the first corporation and the second branch the outcomes of the second corporation.
02

Calculate Probabilities for all outcomes

Next, we calculate probabilities for all outcomes on the tree diagram we drew starting from the root. Each branch will have a probability attached, with the probability of making a donation being .72 and not making a donation being .28 (i.e. 1-.72).
03

Determine the Probability of Desired Outcome

The question asks for the probability that at most one corporation makes charitable contributions. We look for outcomes with at most one corporation donating. These are the DN, ND, and NN outcomes. We calculate their respective probabilities by multiplying the connected branches that lead to them, and add these calculated probabilities together to get .416.

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