Let us assume that all space shuttles will be launched at 81F (which is the high

Question

Let us assume that all space shuttles will be launched at 81F (which is the highest recorded launch temperature in Figure 1.3).With this temperature, the probability of an O-ring failure is equal to p(81) = 0.0137 (see Section 1.4 or Exercise 4.8).

(a) What is the probability that during 23 launches no O-ring will fail, but that at least one O-ring will fail during the 24th launch of a space shuttle?

(b) What is the probability that no O-ring fails during 24 launches?

The solution says:

I don't understand where the 6 comes from.

I thought for a] it would just be 1-p(1-p)^23

4.8 b Since X has a Bin (6, 0.8178) distribution, we find that P(X 2 1) 1 P (X 4.9 a With these assumptions, X has a Bin (6, 0.0137) distribution so we find that the probability that during a launch at least one O-ring fails is equal to PCX 21) 1 PCX 0) 1 (1 0.0137)6 0.079436. But then the proba. bility, that at least one O-ring fails for the first time during the 24th launch is equal to (PCX 0)) TPOX 1) 0.011 84.

Explanation / Answer

here all the answers are fine.

The given data follows binomial distribution

I have verified your problem through internet.

You have missed the number of o-rings

(see Section 1.4 or Exercise 4.8); from this

number of o-rings = 6 (trails)

so '6' is correct

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