The bag contains three red marbles, two blue marbles, and seven yellow marbles. Two marbles are randomly drawn from the bag. What is the probability of drawing a blue marble, replacing it, and then drawing a yellow marble
To calculate the probability of drawing a blue marble, replacing it, and then drawing a yellow marble, we need to consider the total number of marbles and the number of favorable outcomes.
The total number of marbles in the bag is given as 3 red + 2 blue + 7 yellow = 12 marbles.
To calculate the probability of each individual event, we need to consider the number of favorable outcomes divided by the total number of outcomes.
First, the probability of drawing a blue marble with replacement is calculated as follows:
Number of blue marbles = 2
Total number of marbles = 12
Probability of drawing a blue marble = 2/12 = 1/6
Since we are replacing the drawn blue marble back into the bag, the number of blue marbles remains the same at 2.
Now, for the second event, the probability of drawing a yellow marble is calculated similarly:
Number of yellow marbles = 7
Total number of marbles = 12
Probability of drawing a yellow marble = 7/12
Since the two events are independent (the outcome of the first marble draw does not impact the second draw since we are replacing), we can find the probability of both events occurring by multiplying their individual probabilities:
Probability of drawing a blue marble and then a yellow marble = (1/6) * (7/12) = 7/72
Therefore, the probability of drawing a blue marble, replacing it, and then drawing a yellow marble is 7/72.