Question

A bag contains 6 blue marbles, 8 white marbles, and 5 black marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a blue marble and then a black marble?

Answer 1

The probability of drawing first a blue marble and then a black marble from a bag with replacement is 30/361, which is approximately 8.31%.

Step-by-step explanation:

To calculate the probability of drawing first a blue marble and then a black marble from a bag containing 6 blue marbles, 8 white marbles, and 5 black marbles with replacement, we need to consider the two independent events separately.

First, we calculate the probability of drawing a blue marble. Since there are 6 blue marbles out of a total of 19 marbles (6 blue + 8 white + 5 black), the probability of drawing a blue marble is 6/19.

Next, because the marble is replaced, the total number of marbles and the number of black marbles in the bag remains the same for the second draw. The probability of drawing a black marble is thus 5/19.

As these two events are independent, we multiply the probabilities of the two events occurring in sequence. Therefore, the probability of drawing a blue marble first and then a black marble after replacing the first is:

(6/19) × (5/19) = 30/361.

This probability simplifies to approximately 0.0831, or 8.31%.