Answer:The chances of drawing a blue on both draws is (3/7)^2 or 9/49, and the chances of getting red on both draws is (4/7)^2 or 16/49. But there are other possible outcomes which have to be considered to come to the correct answer.
There are 4 possible outcomes, as follows (although the chances of these outcomes are different):
Comb Chances
RR …….. 16/49
RB …….. 12/49
BR …….. 12/49
BB ……… 9/49
total …….. 49/49
So we can say that the chances of drawing red marbles on each draw are 16/49, and the chances of drawing blue ones on each draw are 9/49. But what about the chances of drawing either both red OR both blue?
I believe we can simply add the 2 probabilities together to come up with a probability of 25/49 that both marbles will match. To check this, let’s figure the probability that the marbles don’t match. There are 2 possible outcomes that will fit this description: BR and RB. The chances of each occurring are 12/49, but since they can be drawn in 2 separate ways, the total probability of drawing 2 unmatched marbles is 24/49, which is 1 - 25/49
So the probability of coming up with a matching pair of marbles after the 2 draws is 25/49
Explanation: