a bag contains 3 blue marbles 9 green marbles and 11 yellow marbles twice you draw a marble and replace it. find P(blue, then green)
The probability of drawing a blue marble and then a green marble is equal to the product of the probability of drawing a blue marble on the first draw (which is 3/23, since there are 3 blue marbles out of 23 total marbles) and the probability of drawing a green marble on the second draw (which is also 9/23, since we replaced the first marble).
Therefore, P(blue, then green) = (3/23) x (9/23) = 27/529.
The answer is 27/529.
To find the probability of drawing a blue marble followed by a green marble, we will use the concept of independent events.
Step 1: Determine the probability of drawing a blue marble.
The bag contains a total of 3 blue marbles out of 3+9+11=23 marbles.
Probability of drawing a blue marble = Number of blue marbles / Total number of marbles
= 3 / 23
Step 2: Determine the probability of drawing a green marble.
The bag contains a total of 9 green marbles out of 23 marbles.
Probability of drawing a green marble = Number of green marbles / Total number of marbles
= 9 / 23
Step 3: Determine the probability of drawing a blue marble followed by a green marble.
Since the marble is replaced after each draw, drawing a blue marble and then a green marble are independent events.
Probability of drawing a blue marble, then a green marble = Probability of drawing a blue marble × Probability of drawing a green marble
= (3/23) × (9/23)
≈ 0.055
Therefore, the probability of drawing a blue marble, then a green marble is approximately 0.055.