Reference no: EM132855199

A pressure vessel flange is designed to be fastened using 5 bolts. Due to factor of safety considered in the design process, it can withstand the design pressure as long as at least 4 of the bolts are intact.

The bolts are drawn simultaneously at random from a box containing 100 bolts, and three bolts in each box are known to be faulty (faulty bolts are those that will certainly fail under the design pressure).

We are interested in finding out the probability that the pressure vessel will fail (Event A).

-Let X be a random variable that denotes the number of bad bolts in the batch of 5 bolts. What are the possible values X can take?

-How would you calculate the probability P(X=1) (also written as P(X-1(1)) or P({s ∈ S|X(s) =1}) or px(1)? How would you calculate the probability P(X-1(2))?

-Plot the probability mass function of X(i.e., a stem plot of x vs px(x)). Make sure that the plots are legible and the axes are labeled.

-Write Event A in terms of X and calculate the required probability.