Question 1207715: Alex chooses a number at random from the set $\{1, 2, 3, \dots, 10\}.$ Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is at least 6?
Answer by mccravyedwin(406)   (Show Source):
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We find the probability of the complement event. (product < 6)
There are 2 ways they can choose different numbers. That is, each of the
ways one of them can choose a 1 and the other choose 2,3,4, or 5. That's
2x4=8 ways.
There are 2 ways they can both choose 1's or both choose 2's.
That's 8+2 or 10 ways to fail.
There are 10 ways for Alex to choose a number and 10 ways for
Winnie to choose a number. That's 10x10 or 100 ways.
The probability of a failure is 10 ways out of 100, or 10/100 or 1/10.
So the probability of a success is 9/10.
Edwin
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