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15 Coupons are numbered from 1......15, 7 Coupons are selected Randomly One at a time With Replacement. The Probability That largest number appearing on selected coupons is 9 is?

How to approach this one?

I know in sample space there will be 15^7 because it is replacement but How can i select that event?

John Lucas
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    Hint: What's the probability that the max is $≤9$? What's the probability that it is $≤8$? – lulu Jul 06 '19 at 10:38

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To count the number of draws whose largest number is exactly $9$, we count the number of draws that have all numbers $9$ or fewer – $9^7$ – and then subtract from that the number of draws that have all numbers $8$ or fewer – $8^7$. The result of this subtraction is the number of draws that have at least one $9$ and no higher numbers, so the final probability is $\frac{9^7-8^7}{15^7}$.

Parcly Taxel
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