Question

There are 100 gumdrops. 78 of them are large, and the rest are small. 33 of them are red, and the rest are other colors. 16 of the gumdrops are large red ones. You choose 1 gumdrop at random, and it is that yummy red color. What is the probability that the gumdrop is large, given that it is red?

Answer 1

you pick one at random, and you know it is red. so it is one of the 33 and that is your denominator. of those 33, 16 are red and that is your numerator.

this is easy if you know how to draw a venn diagram. make two large circles that overlap. one label "large" and the other "red" we start in the center.
16 are large and red so fill in the overlap of the circle with 16. there are 33 red total, and we have accounted for 16 of them so the rest of the red circle outside of the intersection has 33-16=17 in it.
likewise the rest of the circle labeled "large" has 78-16=62
we have accounted now for 62+ 16 + 17 =95 gumballs so outside both circle is the remaining 5
this is probably too much work for this simple problem, but it gives a complete picture.

Answer 2

alot of work for this one but it makes sense at the end! thnx