Probability of selecting a purple marble and then a white marble:
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 in the bag. After drawing a purple marble and not replacing it, there will be 8 marbles left in the bag with 2 white ones. Therefore, the probability of drawing a white marble on the second draw is 2/8 or 1/4.
To find the probability of both events happening together, we multiply the probabilities:
(7/9) x (1/4) = 7/36
Therefore, the probability of selecting a purple marble and then a white marble is 7/36.
Probability of selecting two white marbles:
The probability of selecting a white marble on the first draw is 2/9, since there are 2 white marbles out of 9 total marbles in the bag. After drawing a white marble and not replacing it, there will be 8 marbles left in the bag with only 1 white one. Therefore, the probability of drawing another white marble on the second draw is 1/8.
To find the probability of both events happening together, we multiply the probabilities:
(2/9) x (1/8) = 1/36
Therefore, the probability of selecting two white marbles is 1/36.
Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row?
To compare the probabilities, we need to find the probability of selecting a purple marble and then another purple marble.
The probability of drawing a purple marble on the first draw is 7/9. After drawing a purple marble and not replacing it, there will be 8 marbles left in the bag with 7 purple ones. Therefore, the probability of drawing another purple marble on the second draw is 7/8.
To find the probability of both events happening together, we multiply the probabilities:
(7/9) x (7/8) = 49/72
Therefore, the probability of selecting two purple marbles in a row is 49/72, which is greater than the probability of selecting two white marbles in a row (1/36).
Therefore, there is a greater chance of selecting two purple marbles in a row than two white marbles in a row.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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.
What is the probability of selecting a purple marble and then a white marble?
What is the probability of selecting two white marbles?
Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work.
3 answers
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1. Probability of purple then white = (7/9) x (1/4) = 7/36
2. Probability of two white marbles in a row = (2/9) x (1/8) = 1/36
3. Probability of two purple marbles in a row = (7/9) x (7/8) = 49/72
Therefore, the probability of selecting two purple marbles in a row is greater than the probability of selecting two white marbles in a row.
2. Probability of two white marbles in a row = (2/9) x (1/8) = 1/36
3. Probability of two purple marbles in a row = (7/9) x (7/8) = 49/72
Therefore, the probability of selecting two purple marbles in a row is greater than the probability of selecting two white marbles in a row.