SOLUTION: two integers from 1 to 10 are randomly selected. the same number may be chosen twice. what is the probability that both numbers are less than 9

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Question 289119: two integers from 1 to 10 are randomly selected. the same number may be chosen twice. what is the probability that both numbers are less than 9
Answer by jim_thompson5910(35256) (Show Source):
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Note: there are 10 numbers to choose from total in the range from 1 to 10.

Since the only two numbers that are NOT less than 9 is 9 itself and 10, this means that there are 8 numbers that are less than 9 (since 10-2=8)

P(number is less than 9) means "the probability that the number is less than 9"

P(number is less than 9) = number of numbers that are less than 9 from 1 to 10/total number of numbers = 8/10 = 4/5

So the probability of choosing ONE number that is less than 9 is 4/5. However, we want to know what the probability of choosing two numbers. So we need to slightly change the probability to:

P(choosing two numbers less than 9) = P(choosing number less than 9 AND choosing number less than 9) = P(number is less than 9)*P(number is less than 9) = (4/5)*(4/5) = 16/25

So the probability is 16/25 which in decimal form is 0.64 or an 64% chance.