First slide

Theorems of probability

Question

Fifteen coupons ate numbered 1, z, 3, 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on selected coupon is 9 is

Moderate

A

$(9 / 16)^{6}$
B

$(8 / 15)^{7}$
C

$(3 / 5)^{7}$
D

None of these

Solution

Since there are 15 possible cases for selecting a coupon and seven coupons are selected, the total number of
cases of selecting seven coupons is $15^{7}$ . It is given that the largest number on the selected coupon is g. Therefore, the
selection is to be made from the coupons numbered 1 to 9. This can be made in $9^{7}$ ways. out of these $9^{7}$ cases, $9^{7}$ cases do not
contain the number 9. Thus, the favorable number of cases is $9^{7} - 8^{7}$ . Hence, the required probability is $(9^{7} - 8^{7}) / (15^{7})$ .

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