Question

A popular coffee shop runs a contest where prize coupons are printed under the rims of its paper cups. Suppose 10% of the cups are printed with a winning coupon, and you purchase 15 cups of coffee during the promotion.
a) What type of distribution best represents this problem? Explain.
b) What is the probability that you will win at least 3 prizes?
c) What is the expected number of prizes you will win?

Answer 1

I would assume a binomial distribution
http://en.wikipedia.org/wiki/Binomial_distribution

Answer 2

thnx i have the notes but i didn't get the answer can u help me p/z

Answer 3

first, what is p, the probability of winning ?

Answer 4

1,2, 3,4,5or 6

Answer 5

10% of the cups are printed with a winning coupon,

try again. p is ?

Answer 6

p is 0.10

Answer 7

and the probability of k wins is
\[\left(\begin{matrix}n \\k\end{matrix}\right)p^k (1-p)^{n-k}\]

Answer 8

What is the probability that you will win at least 3 prizes?
that would be Pr(3)+Pr(4) + ... + Pr(15)

or because we know Pr(0)+Pr(1)+Pr(2) + ...+ Pr(15) =1
it would be easier to figure out
1- (Pr(0) + Pr(1) + Pr(2) )

Answer 9

thnx is this the final answer

Answer 10

c) What is the expected number of prizes you will win?

E(X) = n*p where n is 15 and p is 0.1

Answer 11

1.5

Answer 12

i mean for b ?

Answer 13

for (b) you figure out Pr(0), Pr(1), Pr(2) add them up and subtract from 1

Answer 14

0.1(0)+ 0.1(1)+0.1(2)-1
0.3-1
-1.7
is that true

Answer 15

Probabilities are always between 0 and 1.

I posted the formula for Pr(k) up above. See wikipedia for details.
or if you need more info, Khan is excellent. See
http://www.khanacademy.org/math/probability/random-variables-topic/binomial_distribution/v/binomial-distribution-1

Answer 16

1-0.3=0.7
thnx so much

Answer 17

u really help me

Answer 18

Here is how to do Pr(0)
\[\left(\begin{matrix}15 \\ 0\end{matrix}\right)0.1^0 0.9^{15}\]

type into the google search window
(15 choose 0) * 0.1^0 * 0.9^15=

you get 0.205891132 for Pr(0)

can you do that for Pr(1)?

Answer 19

i got 1.3

Answer 20

(15 choose 1) * 0.1^0 * 0.9^15=

Answer 21

(15 choose 0) * 0.1^0 * 0.9^15=0.20589113209

Answer 22

finlly i got it thnx