Find the requested probability.

A box contains the following mixture of colored marbles: 2 black, 1 red, 4 yellow, and 2 green. If two marbles are drawn, the second being drawn after the first is replaced, then what is the probability that both are yellow?

Hi i was wondering if someone could help me

To find the probability that both marbles drawn are yellow, we need to set up the probability calculation.

Step 1: Determine the total number of marbles in the box.
In this case, there are 2 black + 1 red + 4 yellow + 2 green = 9 marbles in total.

Step 2: Determine the number of yellow marbles in the box.
The box contains 4 yellow marbles.

Step 3: Calculate the probability.
Since the marbles are drawn with replacement, the probability of drawing a yellow marble for each draw is the same.

The probability of drawing a yellow marble on the first draw is 4/9 since there are 4 yellow marbles out of a total of 9 marbles.

The probability of drawing a yellow marble on the second draw is also 4/9, as the first marble is replaced and the number of marbles remains the same.

To find the probability of both events happening (finding yellow on both draws), we multiply the individual probabilities together.

P(Both are yellow) = P(First marble is yellow) * P(Second marble is yellow)
P(Both are yellow) = (4/9) * (4/9) = 16/81

Therefore, the probability that both marbles drawn are yellow is 16/81.

To find the probability of drawing two yellow marbles, we need to compute the probability of drawing a yellow marble on the first draw and then drawing another yellow marble on the second draw.

The probability of drawing a yellow marble on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the box:

Probability of drawing a yellow marble on the first draw = Number of yellow marbles / Total number of marbles

In this case, there are 4 yellow marbles and a total of 9 marbles in the box. So,

Probability of drawing a yellow marble on the first draw = 4 / 9

Since the marble is replaced after the first draw, the probability of drawing another yellow marble on the second draw is the same as the probability of drawing a yellow marble on the first draw. Thus,

Probability of drawing a yellow marble on the second draw = Probability of drawing a yellow marble on the first draw = 4 / 9

To find the probability that both marbles drawn are yellow, we need to multiply the probabilities of both events happening:

Probability of drawing two yellow marbles = Probability of drawing a yellow marble on the first draw * Probability of drawing a yellow marble on the second draw

So, substituting the values,

Probability of drawing two yellow marbles = (4 / 9) * (4 / 9) = 16 / 81

Therefore, the probability of drawing two yellow marbles is 16 / 81.

there are 9 marbles , with 4 being yellow

the probability of drawing a yellow is ... 4 / 9

the two drawings are independent events
... the 1st drawing doesn't affect the 2nd

the probability of two yellows is the product of the individual drawings

p(2 y) = 4/9 * 4/9