Given that, a certain kind of component will survive a given shock
Let p be the probability that component survives the shock test.
If p is the probability that component survives the shock test, then q is the probability that the component doesn’t survive the shock test.
⇒ p + q = 1
⇒ q = 1 – p
Let X denote a random variable that represents the components that survive the shock test out of the 5 components tested.
The probability that r components out of n components survive the shock test is given by the binomial distribution.
P (X = r) = nCrprqn-r
Here, n = 5 (sample components tested)
We can re-write it as,
(i). We need to find the probability that among 5 components tested exactly 2 will survive.
Then, put r = 2 in equation (A). We have
⇒ P (X = 2) = 0.0879
∴, the probability that exactly 2 components out of 5 will survive the test is 0.0879.
(ii). We need to find the probability that among the 5 components tested at most 3 will survive.
So, this can be give in two ways:
(a). Probability that out of 5 components at most 3 will survive = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)
(b). Probability that out of 5 components at most 3 will survive = 1 – [P (X = 4) + P (X = 5)]
Let us solve it by using the formula in (b).
So, let us find out P (X = 4).
Putting r = 4 in equation (A), we get
Now, let us find out P (X = 5).
Putting r = 5 in equation (A), we get
Using the values of P (X = 4) & P (X = 5) in formula (b), we get
⇒ Probability = 0.3672
∴, the probability that out of 5 components at most 3 will survive is 0.3672.
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