Question

A bag contains 28 blue marbles and 12 red marbles. If Milton removes two marbles without replacing them, what is the probability that the first marble will be blue and the second one will be red?

A.14/65
B.21/100
C.77/390
D.1/4

Answer 1

A: 14/65

Explanation:

Let A be the event of pulling a blue marble first, there are 28 blue marbles

Let B be the event of pulling a red marble second, there are 12 red marbles

There are 40 total marbles in the bag.

So

P(A) = 28/40

Since he pulls two marbles with out replacement, there is one less marble in the bag when he pulls the second marble, so there are only 39 marbles left, so

P(B) = 12/39

When calculating the probability of multiple events, you multiply their probabilities together, so we have

P(A then B) = (28/40)(12/39) = 336/1560

Now reduce the fraction...

112/520

28/130

14/65