"Compare their chances of success" is very vague.
P(A gets k prizes) = $\binom{3}{k}\binom{5}{3-k}/\binom{8}{3}$, k = 0 to 3
P(B gets k prizes) = $\binom{2}{k}\binom{6}{2-k}/\binom{8}{2}$ , k = 0 to 2
Now compare them in whichever way you think the questioner wants !