Question

a box contains the following mixture of colored marbles 2 black, 3 red, 5 yellow, and 2 green. If two marbles are drawn, the second being drawn n after the first is replaced, then what is the probability that both are black?

Answer 1

(2/12)^2 = ?

Answer 2

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To find the probability of drawing two black marbles, we need to determine the total number of marbles and the number of black marbles.

Total number of marbles = 2 (black) + 3 (red) + 5 (yellow) + 2 (green) = 12 marbles

Number of black marbles = 2

When drawing with replacement, the probability of an event occurring remains the same each time. Therefore, the probability of drawing a black marble on the first draw is 2/12.

Since the marble is replaced, the probability of drawing a black marble on the second draw is also 2/12.

To find the probability of both events happening, we multiply the probabilities: (2/12) * (2/12) = 4/144 = 1/36.

Therefore, the probability of drawing two black marbles with replacement is 1/36.

Answer 4

[AI-generated answer — Explain Bot]

To find the probability of drawing two black marbles, we need to calculate the probability of drawing a black marble on the first draw and then drawing a black marble again on the second draw, assuming the first marble is replaced.

Step 1: Find the probability of drawing a black marble on the first draw.
In this case, there are a total of 2 black marbles out of the total number of marbles in the box. Therefore, the probability of drawing a black marble on the first draw is:
P(1st draw = black) = number of black marbles / total number of marbles
P(1st draw = black) = 2 / (2 + 3 + 5 + 2)
P(1st draw = black) = 2 / 12
P(1st draw = black) = 1/6

Step 2: Find the probability of drawing a black marble on the second draw after replacing the first black marble.
Since we are replacing the first marble after it is drawn, the probability of drawing a black marble on the second draw is the same as the probability of drawing a black marble on the first draw:
P(2nd draw = black) = P(1st draw = black)
P(2nd draw = black) = 1/6

Step 3: Find the probability of both marbles being black.
To find the probability of both marbles being black, we multiply the probabilities of the independent events (drawing a black marble on the first draw and drawing a black marble on the second draw):
P(both black) = P(1st draw = black) * P(2nd draw = black)
P(both black) = (1/6) * (1/6)
P(both black) = 1/36

Therefore, the probability that both marbles drawn are black is 1/36.