Hallo, nice to meet you. I'm quite new on this forum. For your problem, we can use conditional probability theorem : p(red)=0.6=p(red|f)p(f)+p(red|m)p(m) p(f/m)=probability of being f or m, p(red|m)=prob. having a red T-shirt knowing the gender, p(red|f)=0.7, p(red|m)=0.4 Hence, p(m)=1-p(f) and 0.6=...