Suppose that an assembly consists of 16 solder joints and th

Suppose that an assembly consists of 16 solder joints and that unknown to the researcher 5 of these solder joints are cracked. If the researcher randomly chooses a sample of 4 of the solder joints for inspection, then the state space of the number of cracked joints in the sample is {0,1,2, 3, 4}. What is the probability that there will be exactly two cracked solder joints in the researchers\' sample?

Solution

There are 16C4 ways to choose 4 joints.

Now, if you sample four joints and want exactly 2 to be broken, there are 11C2 ways to choose the non broken ones, and 5C2 ways to choose the broken ones. Hence, there are (11C2)(5C2) ways to do it.

Thus,

P = [(11C2)(5C2)]/(16C4) = 0.302197802 [answer]

I think there\'s a typo on OPTION A here. If so, that will be the answer.