Probability Ques 8
- Fifteen coupons are numbered $1,2, \ldots, 15$, 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) $\left(\frac{9}{16}\right)^6$
(b) $\left(\frac{8}{15}\right)^7$
(c) $\left(\frac{3}{5}\right)^7$
(d) None of these
Show Answer
Answer:
Correct Answer: 8.(d)
Solution: (d) Since there are $15$ possible cases for selecting a coupon and seven coupons are selected, the total number of cases of selecting seven coupons $=15^7$
It is given that the maximum number on the selected coupon is $9$ , 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, $8^7$ does not contain the number $9$ .
Thus, the favourable number of cases $=9^7-8^7$.
$\therefore \quad$ Required probability $=\frac{9^7-8^7}{15^7}$
BETA
