A fast food restaurant chain releases cushions in 4 safari animal hoodie designs in addition to your combination meal. A
fan of the cushions is determined to collect them all, and suppose one of the four
designs is randomly given when purchased.Determine the number of meals the fan
is expected to have in order to collect all four designs of the cushion.
The following is my solution:
Let $Y_i$ be the number of meals required for collecting a new cushion.
$Y_0$ means that the fan doesn't collect any cushion. That is to say, the fan just needs one meal to get a new cushion.
$Y_0=1$
$Y_1 \sim Geo(3/4)$
$Y_2\sim Geo(2/4)$
$Y_3\sim Geo(1/4)$
Let $N$ be the number of meals the fan collects all four designs of the cushion.
$E[N]=E[Y_0+Y_1+Y_2+Y_3]=E[Y_0]+E[Y_1]+E[Y_2]+E[Y_3]=1+\frac{4}{3}+\frac{4}{2}+\frac{4}{1}=8.33$.
Is there anything wrong to my solution?
Asked
Active
Viewed 58 times
0
RobPratt
- 45,619
-
3You may also want to look up Coupon Collector Problem ... – Hagen von Eitzen Apr 12 '22 at 09:08
-
You have a typo but $\frac44+\frac43+\frac42+\frac41\approx 8.33$ looks reasonable – Henry Apr 12 '22 at 09:14