jmc

There are $2^4=16$ possible outcomes, since each of the 4 coins can land 2 different ways (heads or tails). If the quarter is heads, there are 8 possibilities, since each of the other three coins may come up heads or tails. If the quarter is tails, then the nickel and dime must be heads, so there are 2 possibilities, since the penny can be heads or tails. So there are $8+2=10$ successful outcomes, and the probability of success is $\frac{10}{16}=\boxed{\frac{5}{8}}$.