A spinner that has equal areas of green, blue, purple, and yellow sections. There’s a bag that has 3 green, 4 blue, and 5 purple marbles. 12 marbles total. If you spin once and draw one marble, what are the odds you will choose different colors?
@“marsha.ss” Note that it doesn’t matter whether you spin the spinner first or draw a marble first because every possibility in the sample space can be represented by a tuple (s, m) (or (m, s)) corresponding to the spinner color and marble color.
The trick here is to notice that no matter what color marble I pick, there is a 3/4 probability that the spinner lands on a different color (if I pick a green marble, then the spinner can land on blue, purple, or yellow). So the probability of getting different colors is 3/4, or 3:1 odds.
of course…ugh. someone else went into a long, convoluted explanation that made no sense to me…this makes perfect sense!
Great – yes, another way you could do it is to spin the spinner first; if you do it that way you obtain 1/4*(3/12 + 4/12 + 5/12 + 1) = 3/4 but is not as slick.