Question

A bag of marbles contains 4 red marbles, 5 green marbles, and 3 blue marbles. Karen pulls two marbles out one after the other without replacing the first marble, what is the probability the first one is red and the second is blue?

Answer 1

The probability that Karen pulls out a red marble first and then a blue marble, without replacement, is 1/11.

Step-by-step explanation:

To calculate the probability that the first marble Karen pulls out is red, and the second one is blue, we take the following steps:

• Determine the total number of marbles: 4 red + 5 green + 3 blue = 12 marbles.
• Calculate the probability of drawing a red marble first: There are 4 red marbles out of 12, so P(first is red) = 4/12 or 1/3.
• After drawing a red marble, there are now 11 marbles left: 3 red, 5 green, and 3 blue.
• Calculate the probability of drawing a blue marble second: Now, since one red marble is removed, there are 3 blue marbles out of 11, so P(second is blue after red) = 3/11.
• To get the overall probability of both events happening in sequence, we multiply the individual probabilities: P(first is red and second is blue) = P(first is red) × P(second is blue after red) = (1/3) × (3/11).
• The result is 3/33 or 1/11.

Therefore, the probability that the first marble is red and the second is blue is 1/11.