Kelly is getting some snacks for a party. a) (1)/(4) of her guests hate peanut butter. Of these, (2)/(3) also hate cola. What fraction of her guests hate both peanut butter and cola? b) (5)/(12) of the guests who don't hate peanut butter are vegetarians. What fraction of Kelly's guests are vegetarians who don't hate peanut butter

## Step 1:We obtain the fraction of Kelly's guests who hate both peanut butter and cola if of her guests hate peanut butter, and of those, also hate cola. We achieve this by multiplication because, mathematically, the "and" corresponds to multiplication when it comes to probabilities and fractions.### ## Step 2:Let's find the fraction of guests that are vegetarians and do not hate peanut butter. Here, of her guests who don't hate peanut (that is one minus the hateful guests or are don't hate peanut butter) are vegetarians.So we multiply ###