Math CentralQuandaries & Queries


Question from Fatima, a parent:

Tamika selects two different numbers at random from the set{8,9,10}and adds them. Carlos takes two different numbers
at random from the set {3,5,6}and multiplies them.What is the probability that Tamika's result is greater than Carlo's result
Please help me to solve this problem.

Hi Fatima,

Tamika can select 8 and 9, 8 and 10 or 9 and 10, each with the same probability, $\large \frac13.$ What are the three sum Tamika can obtain? What are the three products Carlos can obtain?

There are thus 9 possible pairs of a sum and a product, each with the same probability. How many of them have the product greater than the sum?


Fatima wrote back

My doubt is that Iam getting only 6 possible Pairs
Please show me all the possible pairs
Thank you very much


If the three sums were a, b and c and the three products were p, q and r then the nine pairs are

ap; aq; ar; bp; bq; br; cp; cq; cr


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