Question

There is a bag filled with 4 blue and 5 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 2 that are different in colour?

Answer 1

5/9

Explanation:

blue marbles = 4

red marbles = 5

total marbles = 4 + 5 = 9

1st marble is taken at random and not replaced.

If the first marble taken is red, then P(red) = 5/9

If the second marble taken is blue, then P(blue) = 4/8 (as there are now 1 less marbles in the bag)

So P(red and blue) = 5/9 x 4/8 = 5/18

If the first marble taken is blue, then P(blue) = 4/9

If the second marble taken is red, then P(red) = 5/8

So P(blue and red) = 4/9 x 5/8 = 5/18

So the probability of getting "red and blue" OR "blue and red" = 5/18 + 5/18 = 5/9