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counting and probability intermediate
Problem
Five balls are numbered 1 through 5 and placed in a bowl. Josh will randomly choose a ball from the bowl, look at its number and then put it back into the bowl. Then Josh will again randomly choose a ball from the bowl and look at its number. What is the probability that the product of the two numbers will be even and greater than 10? Express your answer as a common fraction.
Solution
There are a total of possibilities. Multiplying or by any of the other numbers in the bowl will not result in a number greater than so we know that Josh does not draw or Therefore, Josh must draw a in order for the result to be even. Thus, his possibilities are: , making for 5 possibilities, and a probability of
Final answer
\frac{1}{5}