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Fifteen coupens are numbered 1,2,3,...15...

Fifteen coupens are numbered `1,2,3,...15` respectively. Seven coupons are selected at random one at a time with replacement The Probability that the largest number appearing on a selected coupon is 9 is :

A

`((9)/(196))^(6)`

B

`((8)/(15))^(7)`

C

`((3)/(7))^(7)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Since, there are 15 possible cases for selecting a coupor and seven coupons are selected, the total number o cases of selecting seven coupons =`15^7`
It is given that the maximum ·number on the selecte coupon is 9, therefore the selection is to be made from the coupons numbered 1 to 9. This can be made in r ways. Out of these `9^7` cases `8^7` does not contain the number 9.
Thus, the favourable number of cases `=9^7-8^7`
`therefore` Required probability `=(9^7-8^7)/(15^7)`
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