Question

A bag contains 9 red marbles, 8 white marbles, and 6 blue marbles. Randomly choose two marbles, one at a time, and without replacement. Find the following:

a) The probability that the first marble is red and the second is white.

Answer 1

The probability of drawing a red marble first and a white marble second, without replacement, from a bag of 23 total marbles is ⅜, which is approximately 14.5%.

Step-by-step explanation:

The problem involves calculating the combined probability of two dependent events: drawing a red marble first and then a white marble, without replacement. The total number of marbles is 9 (red) + 8 (white) + 6 (blue) = 23 marbles.

First, calculate the probability of drawing a red marble:

• P(Red first) = ⅔

Since one red marble has been drawn, there are now 22 marbles left. Next, determine the probability of drawing a white marble:

• P(White second | Red first) = ⅘

To get the combined probability, multiply the two individual probabilities:

• P(Red first and White second) = P(Red first) × P(White second | Red first) = ⅔ × ⅘ = ⅜

So, the probability that the first marble is red and the second is white is ⅜ or about 14.5%