Need some help with these questions

Don't know how to start #1

For #5 I just found the probability that among the 3 chosen, at least 1 shows signs of burning using the binomial distribution i.e.

P(a shipment is held back) = P(at least one of the 3 burns) = P(exactly 1 burns) + P(exactly 2 burn) + P(exactly 3 burn) = 0.488

I am wondering if this is correct? How do I use the information about the phones being in boxes of 12 in the calculation?

This post was edited by Bloo_Guardian on Nov 16 2016 08:55pm

For 5, you're correct.

The information of the 12 phones per box is not relevant, it's always 48.8%

For 2, you can compute for k = 0 ... 6 the probability for exactly k customers to come, using the binomial law.
Then compute the corresponding profit P according to the number m of pies cooked :

if k = 0, P = - 8*m
if k = 1, P = 12 - 8*m
if k = 2, P = 24 - 8*m, unless m = 1 (then only 1 is sold and P = 4),
and so on.

Finally, multiply each probability by the corresponding profit P.

Example with m = 2 :

k=0 | prob = (2/3)^6 | P = -16
k=1 | prob = 6*(1/3)*(2/3)^5 | P = -4
k=2 | prob = 15*(1/3)^2*(2/3)^4 | P = 8
k=3 | prob = 20*(1/3)^3*(2/3)^3 | P = 8
k=4 | prob = 15*(1/3)^4*(2/3)^2 | P = 8
k=5 | prob = 6*(1/3)^5*(2/3) | P = 8
k=6 | prob = (1/3)^6 | P = 8
leads to : expecting profit ~ 2.7325 $

Thank you