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.