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.
done, look at your later post.
I'll start 3 for you.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(2W) = 2/9 * (2-1)/(9-1)
P(2P) = 7/9 * (7-1)/(9-1)
Either-or probabilities are found by adding the individual probabilities.
Sure! Let's break down each question step-by-step:
1. The probability of selecting a purple marble and then a white marble can be calculated by multiplying the probabilities of the two events.
Step 1: Calculate the probability of selecting a purple marble:
There are a total of 2+7=9 marbles in the bag, and 7 of them are purple. Therefore, the probability of selecting a purple marble on the first draw is 7/9.
Step 2: Calculate the probability of selecting a white marble (after selecting a purple marble without replacement):
After drawing the first purple marble, there are now 1 white marble left out of the remaining 8 marbles. Therefore, the probability of selecting a white marble on the second draw is 1/8.
Step 3: Multiply the probabilities calculated in Steps 1 and 2:
(7/9) * (1/8) = 7/72
So, the probability of selecting a purple marble and then a white marble is 7/72.
2. The probability of selecting two white marbles can also be calculated similarly by multiplying the probabilities of the two events.
Step 1: Calculate the probability of selecting a white marble on the first draw:
There are a total of 2+7=9 marbles in the bag, and 2 of them are white. Therefore, the probability of selecting a white marble on the first draw is 2/9.
Step 2: Calculate the probability of selecting a white marble (after selecting a white marble without replacement):
After drawing the first white marble, there is now 1 white marble left out of the remaining 8 marbles. Therefore, the probability of selecting a white marble on the second draw is 1/8.
Step 3: Multiply the probabilities calculated in Steps 1 and 2:
(2/9) * (1/8) = 1/36
So, the probability of selecting two white marbles is 1/36.
3. To determine whether there is a greater chance of selecting two white marbles in a row or two purple marbles in a row, compare the probabilities calculated in Questions 1 and 2.
The probability of selecting a purple marble and then a white marble (Q1) is 7/72, while the probability of selecting two white marbles (Q2) is 1/36.
Therefore, the probability of selecting two white marbles (Q2) is greater than the probability of selecting a purple marble and then a white marble (Q1).
Sure, I can help you understand how to solve these probability questions.
1. What is the probability of selecting a purple marble and then a white marble?
To calculate the probability of multiple independent events occurring in sequence, you need to multiply the probabilities of each individual event.
In this case, the probability of drawing a purple marble on the first draw is 7/9 (since there are 7 purple marbles out of 9 total marbles). After drawing a purple marble, there are now 8 marbles left in the bag, including 2 white marbles. So the probability of drawing a white marble on the second draw is 2/8.
To find the probability of both events happening sequentially, you multiply the probabilities: (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. What is the probability of selecting two white marbles?
Similar to the previous question, you need to multiply the probabilities of each individual event.
The probability of drawing a white marble on the first draw is 2/9. After drawing a white marble, there are now 8 marbles left in the bag, including 1 white marble. So the probability of drawing another white marble on the second draw is 1/8.
To find the probability of both events happening sequentially, you multiply the probabilities: (2/9) * (1/8) = 2/72 = 1/36.
Therefore, the probability of selecting two white marbles is 1/36.
3. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row?
To answer this question, we compare the probabilities we calculated in the previous two questions.
P(White, White) = 1/36 (probability of selecting two white marbles in a row)
P(Purple, Purple) = 0 (since there are only 2 white marbles in the bag)
As we can see, the probability of selecting two purple marbles in a row is 0, while the probability of selecting two white marbles in a row is 1/36. Therefore, there is a greater chance of selecting two white marbles in a row than two purple marbles in a row.