In a semiconductor manufacturing process, three wafers from a lot are tested. each wafer is classified as pass or fail. assume that the probability that a wafer passes the test is 0.7 and that wafers are independent. determine the probability mass function of the number of wafers from a lot that pass the test. round your answers to three decimal places (e. g. 98.765).

Step-by-step explanation:

The probability mass function P(X = x) is the probability that X happens x times.

When n trials happen, for each , the probability mass function is given by:

In which p is the probability that the event happens.

is the permutation of n elements with x repetitions(when there are multiple events happening(like one passes and two not passing)). It can be calculated by the following formula:

The sum of all P(X=x) must be 1.

In this problem

We have 3 trials, so

The probability that a wafer pass a test is 0.7, so

Determine the probability mass function of the number of wafers from a lot that pass the test.

answer: 45

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