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.

f is the midpoint of

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: