Question 625534
Let x denote the number of heads.

1. *[tex \LARGE P(x = 4) = {{5}\choose{4}} (\frac{1}{2})^5 = \frac{5}{32}]

2. and 3. are pretty easy. By symmetry, P(x = 3) = P(x = 2) because the probability of obtaining a head and a tail is the same. Similarly, P(x = 4) = P(x = 1) and P(x = 5) = P(x = 0).

Therefore, without doing any calculations, we can say that P(x >= 3) and P(x <= 2) are both equal, and they are equal to 1/2.