15 coupons are numbered 1,2,3…15. 7 coupons are selected at random one at a time with replacement. Find probability that 9 is the largest number appearing on the coupon.
I am having a problem finding $N(a)$ for this problem.
My working:
$N(s)= 15^7$ (since you have 15 choices for each time you pick up a coupon)
$N(a)= 9^7$ (since you have 9 permissible choices for each time you pickup a coupon)
But according to my textbook $N(a)= 9^7 -8^7$ but no further explanation is given.
So i would really appreciate it if someone could point out where i am going wrong. Thanks in advance 🙂
Best Answer
$9^7$ are the possibles 7-uples, but you want that at least one is 9. The competent of this is the 7-uples such that all elements aren't 9, there are $8^7$