The Magazine Mass Marketing Company has received 12 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.6. What is the probability that more than a fourth of the entry forms will include an order? Round your answer to four decimal places.

And we can find the individual probabilities like this:

And replacing we got:

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:  

For this case we want this probability:

Since one fourth of the total number 12 is 12/4 =3

We can find this probability using the complement rule:

And we can find the individual probabilities like this:

And replacing we got:

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

b is the correct answer