Probability problem

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Genevie

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A random sample of 6 items is taken from a large consignment and tested in two independent stages. The probability that an article will pass either stage is q. All six items are first tested at stage 1, and provided 5 or more pass, those which pass are retested at stage 2. The consignment is accepted if there is no more than one failure at each stage. Find expressions in terms of q for:
a) The probability that stage 2 of the test will be required.
b) The number of items expected to undergo stage 2.
c) The probability P(q) of accepting the consignment.
(d) Show that dP d q = 0 when q = 1 and find P(q = 0.9) and P(q = 0.8). Comment on your results.

a) P(stage2) = P(x>=5) = P(x=5) + P(x=6)
b) (a) E(x>=5) = E(5)+E(6)
c) P(X=x) = q^x * (1-q)^1-x
d)


Please help, I’m not sure of my answers
 
Where did "q" go? "Find expressions in terms of q..."

P(x=5) = ??
P(x=6) = ??

Consider (q+p)^6
 
tkhunny said:
All of them. What I suggested, if you expand it, will specify the entire distribution.
Click to expand...
a) P(stage2) = P(x>=5) = (p+q)^5+ (P+q)^6
b) (a) E(x>=5) = E(5)+E(6)
c) P(X=5)= q^5* (1-q)^1-x
P(X=6) = q^6* (1-q)^0
d)
 
You didn't expand it.

(q+p)^6 gives seven terms. Those terms are p(6), p(5), p(4), …, p(0)
 
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