Question
Fifteen coupons are numbered 1, 2 . . . . . 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
Answer :
$${\left( {\frac{3}{{5}}} \right)^7}$$
Solution :
$$n = 7$$
Prob. of getting any no. out 1, 2, 3, . . . . 9 is $$p = \frac{9}{{15}}$$
$$\therefore \,\,q = \frac{6}{5}$$
$$P\left( {x = 7} \right) = \,{\,^7}{C_7}{p^7}{q^0}$$ [Binomial distribution]
$$\eqalign{
& = {\left( {\frac{9}{{15}}} \right)^7} \cr
& = {\left( {\frac{3}{5}} \right)^7} \cr} $$