Question

A coin is tossed 8 times. each outcome is a sequence of 8 heads and/or tails. what is the number of possible outcomes where the number of heads is exactly 3? at least 6? at most 3?

Answer 1

Using a calculator with the binompdf and binomcdf features, I can calculate these values. My calculator is a TI-83 plus, and the features are found under the 2nd, Vars keys (Scroll up or down until you see them).

If "exactly" is to be found, use binompdf: 
binompdf(number of trials, probability of success, exactly number)

ANSWER for exactly 3: binompdf(8, 0.5, 3) = 0.21875 = 21.875%

If "at least" is to be found, use binomcdf:
binomcdf(number of trials, probability of success, at least number - 1)

ANSWER for at least 6: binomcdf(8, 1/2, 5) ≈ 0.8555 ≈ 85.55%

If "at most" is to be found, use binomcdf:
binomcdf(number of trials, probability of success, at most number)

ANSWER for at most 3: binomcdf(8, 0.5, 3) ≈ 0.3633 ≈ 36.33%