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33 votes
33 votes
There is a bag filled with 3 blue and 4 red marbles.

A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting at least 1 red?

User Charlesdarwin
by
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1 Answer

23 votes
23 votes

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:

User Nikolay Bronskiy
by
2.6k points