In a certain shipment of 20 televisions, 9 are defective. 16 of the televisions are selected at random without replacement. What is the probability that 7 of the 16 televisions are defective? Express your answer as a fraction or a decimal number rounded to four decimal places.

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest, on this case we now that:  

The probability mass function for the Binomial distribution is given as:  

Where (nCx) means combinatory and it's given by this formula:  

And for this case we want to calculate the following probability:

Using the probability mass function we have this: