Question

Spoke Weaving Corporation has eight weaving machines of the same kind and of the same age. The probability is that any weaving machine will break down at any time. Find the probability that at any given time none of the weaving machines will be broken down. Round your answer to four decimal places.

Answer 1

Explanation:

Some information in this question is missing as we are not given with the probability p that any weaving machine will break down anytime.

For solving this question, Suppose the probability p = 0.2

n = no. of machines

p = probability of breaking at any time and

x = the number of successes and

Let A be a random variable that denotes the number of weaving machines that will break down.

A follows binomial distribution with n = 8 and p = 0.2

We will use the formula P(A=x) = nCx *
`p^(x)` *
`(1-p)^(n-x)`

Now, the probability that at any given time none of the weaving machines will be broken down:

P (A=0) = 8C0 *
`0.2^(0)` *
`(1-0.2)^(8-0)`

P = 1 * 1 * 0.1677

P (A=0) = 0.1677

So, the probability that at any given time none of the weaving machines will be broken down is 0.1677.