If x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?

Which methods of obtaining binomial probabilities are you familiar with?  You could use a TI-83 or TI-84 Plus calculator's binompdf(    ) function, or obtain this probability from a binomial probability table, or calculate the probability using the appropriate formula.

Using my TI-83 Plus calculator:  type in binompdf(10, 0.8, 4).  My calculator returns the result 0.0055.  This is a "small" probability.

As an example, try letting n=8 instead of 4:  binompdf(10, 0.8, 8).  My calculator returns the result 0.3020.

One more example:  use the "binomcdf" function to produce all nine probabilities (x=0 through x=8):  {1.02E(-7), 4.096E(-6),  0.0055, 0.0264, 0.0881, 0.2013, .3020, 0.2684, 0.1774}.    The outcome "8" has the greatest probability.  Were you to add up these 11 probabilities, the sum would be 1.