Consider both the sum and the product for the desired events.
See solution.
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We are asked to write a probability problem using the sample space represented by the tree diagram.
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Problem
Consider that we have two boxes, Box A and Box B. Suppose that there are pieces of paper with numbers written on them in each box. Box A contains the numbers 1, 2, and 3, while Box B contains the numbers 1 and 2. We randomly draw one of the numbers from each box. Let's list the possible outcomes.
cc
(1,1) & (1,2)
(2,1) & (2,2)
(3,1) & (3,2)
In each ordered pair, the first number is the number drawn from Box A and the second number is the number drawn from Box B. We want to find the probability that either the sum or the product of the numbers drawn is 3. Let's list all the possible sums and products.
Outcome
Sum
Product
(1,1)
1+1 = 2
1* 1 = 1
(1,2)
1+2 = 3
1* 2 = 2
(2,1)
2+1 = 3
2* 1 = 2
(2,2)
2+2 = 4
2* 2 = 4
(3,1)
3+1 = 4
3* 1 = 3
(3,2)
3+2 = 5
3* 2 = 6
We can see that there are 6 total possible outcomes and 3 of those outcomes have a sum or a product of 3. Let's find the probability that the sum or product of the drawn numbers is 3.
P(sum or product of3) = favorable outcomes/total outcomes
