Question

A manufacturer determines that a big screen HDTV set had probability of .8,.15,.05 respectively,
of being placed in the categories: acceptable, minor defect, or major defect. If 3 HDTV's
are inspected:

(a) find the probability that 2 are acceptable and 1 is a minor defect

(b) Find the marginal distribution of the number in minor defect

(c) compare your answes in part (b) with the binomial probabilities b(x;3,.15).comment.

Answer 1

Known information:

P = .8,.15, and .05
f(x)= acceptable, minor defect, and major defect

Here is my attempt so far:

For part (a)
Since the probability of 1 acceptable is .08,

p1+p1= .16

and the probability of a minor defect is p2=.15
so the total probability of 2 acceptable and a minor defect is .16+.15=.31
(I'm not quite sure of I'm suppose to find the total probability or just
for each category seperately)

Answer 2

For part (b) I'm unsure of how to find the marginal distribution it isn't really covered in this section of my book.

Answer 3

for (a) is it 3*9.8)^2 *.15 =.288