Question

Suppose a jar contains 5 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

To find the probability that both marbles are red, we can use the formula for the probability of independent events:

P(A and B) = P(A) * P(B|A)

Here, event A is pulling out a red marble on the first draw, and event B is pulling out a red marble on the second draw, given that we already pulled out a red marble on the first draw.

First, let's find the probability of event A:

There are 5 red marbles and a total of 5 + 14 = 19 marbles in the jar. So the probability of drawing a red marble on the first draw is:

P(A) = 5/19

Now let's find the probability of event B, given that we already drew a red marble on the first draw:

Since we already drew one red marble, there are now 4 red marbles left in the jar, and a total of 4 + 14 = 18 marbles.

P(B|A) = 4/18

Now we can find the probability of both events A and B occurring:

P(A and B) = P(A) * P(B|A)

P(A and B) = (5/19) * (4/18)

P(A and B) = 20/342

Simplify the fraction:

P(A and B) = 10/171

So the probability that both marbles are red is 10/171.