A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn.

1. What is the probability of selecting a purple marble and then a white marble?

2. What is the probability of selecting two white marbles?

3. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work.

Please help I don't understand.

Very basic probability problems

2 white
7 purple, total of 9 marbles
prob(purple) = 7/9
since this marble is not returned, there are now only 8 marbles left
prob(white) = 2/8 or 1/4
So prob(purple, then white) = (7/9)(1/4) = 7/36

in the same way, prob(white, then white) = (2/9)(1/8) = 1/36

you do the last one, let me know what you get.

7th

rose waiiiit are you in 6th grade cause from all of your posts im learning the same exact thing

3. greater chance of choosing purple because there's 7 marbles vs 2

Sure! Let's go through each question step by step.

1. To find the probability of selecting a purple marble and then a white marble, we need to consider the probability of each event happening and then multiply them together.

First, let's find the probability of selecting a purple marble on the first draw.

There are a total of 2 white marbles and 7 purple marbles, so the probability of selecting a purple marble on the first draw is 7/(2+7) = 7/9.

Next, since the first marble is not replaced, the bag now contains one less marble in total. So, for the second draw, the probability of selecting a white marble is 2/(2+6) = 2/8.

To find the probability of both events happening, we multiply the probabilities together:

P(purple then white) = P(purple) * P(white) = (7/9) * (2/8) = 14/72 = 7/36.

Therefore, the probability of selecting a purple marble and then a white marble is 7/36.

2. To find the probability of selecting two white marbles, we again need to consider the probability of each event happening and then multiply them together.

The probability of selecting a white marble on the first draw is 2/(2+7) = 2/9.

Since the first marble is not replaced, there is now one less marble in the bag, and the probability of selecting a white marble on the second draw is 1/(2+6) = 1/8.

To find the probability of both events happening, we multiply the probabilities together:

P(two white marbles) = P(white) * P(white) = (2/9) * (1/8) = 2/72 = 1/36.

Therefore, the probability of selecting two white marbles is 1/36.

3. To compare the chances of selecting two white marbles in a row versus two purple marbles in a row, we can directly compare the probabilities we found in questions 1 and 2.

The probability of two white marbles in a row is 1/36, and the probability of two purple marbles in a row can be calculated using a similar process as in question 1.

The probability of selecting a purple marble on the first draw is 7/9, and since the first marble is not replaced, the probability of selecting another purple marble on the second draw is 6/8.

To find the probability of two purple marbles in a row, we multiply the probabilities together:

P(two purple marbles) = P(purple) * P(purple) = (7/9) * (6/8) = 42/72 = 7/12.

Therefore, the probability of two purple marbles in a row is 7/12, which is greater than the probability of two white marbles in a row (1/36).

Based on the calculations, there is a greater chance of selecting two purple marbles in a row than two white marbles in a row.