Answer
$2.44256\cdot10^{-7}$
Work Step by Step
The chance of doing a specific problem correctly by guessing is $0.25$. Then using the binomial probability distribution, the probability of having $15$ correct is: $_{30}C_{21}(0.25)^{21}(0.75)^{9}=2.44256\cdot10^{-7}$