binomial help, one more.

The probability that a challenger will beat an incumbent senator in the general election is .20. We select ten races at random in which an incumbent and a challenger are running in order to make some predictions about the outcome of the elections.

a) What is the probability that no more than three of the challengers win?
b) What is the probability that at least four of the challengers win?

How do these get set up? I'm worried about getting tripped up on the wording.

twobeatsoff said:

The probability that a challenger will beat an incumbent senator in the general election is .20. We select ten races at random in which an incumbent and a challenger are running in order to make some predictions about the outcome of the elections.
a) What is the probability that no more than three of the challengers win?
b) What is the probability that at least four of the challengers win?

Click to expand...

\(\displaystyle \sum\limits_{k = 4}^{10} {\binom{10}{k}\left( {0.2} \right)^k \left( {0.8} \right)^{10 - k} } \) is the probability that at least four of the challengers win.