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.
a. What is the probability of selecting a purple marble and then a white marble?
b. What is the probability of selecting two white marbles?
c. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work. Answer each question in two-three sentences.
a. The probability of selecting a purple marble first is 7/9, and the probability of selecting a white marble second (without replacing the first marble) is 2/8 (since there are now only 8 marbles left in the bag). Therefore, the probability of selecting a purple marble and then a white marble is (7/9) * (2/8) = 7/36.
b. The probability of selecting a white marble first is 2/9, and the probability of selecting a white marble second (without replacing the first marble) is 1/8 (since there are now only 8 marbles left in the bag and only 1 white marble left). Therefore, the probability of selecting two white marbles is (2/9) * (1/8) = 1/36.
c. There is a greater chance of selecting two purple marbles in a row.
The probability of selecting a purple marble first is 7/9, and since the marble is not replaced, the probability of selecting another purple marble is 6/8 (since there will be one less marble in the bag). Therefore, the probability of selecting two purple marbles in a row is (7/9) * (6/8) = 21/36. This is greater than the probability of selecting two white marbles in a row, which we found to be 1/36.
Answer each question in two sentences
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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.
a. What is the probability of selecting a purple marble and then a white marble?
b. What is the probability of selecting two white marbles?
c. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work. Answer each question in two-three sentences.
a. The probability of selecting a purple marble and then a white marble is 7/36.
b. The probability of selecting two white marbles is 1/36.
c. There is a greater chance of selecting two purple marbles in a row as the probability of selecting two purple marbles is 21/36, which is much greater than the probability of selecting two white marbles at 1/36.
a. To find the probability of selecting a purple marble and then a white marble, we need to multiply the probabilities of each event happening. The probability of selecting a purple marble on the first draw is 7/9. Since one marble is not replaced, the probability of selecting a white marble on the second draw is 2/8. Therefore, the probability of selecting a purple marble followed by a white marble is (7/9) * (2/8) = 7/36.
b. The probability of selecting two white marbles can be found by multiplying the probabilities of each event happening. The probability of selecting a white marble on the first draw is 2/9. Since one marble is not replaced, the probability of selecting another white marble on the second draw is 1/8. Therefore, the probability of selecting two white marbles is (2/9) * (1/8) = 1/36.
c. Comparing the probabilities, we can see that the probability of selecting two white marbles in a row (1/36) is less than the probability of selecting two purple marbles in a row (7/36). Therefore, there is a greater chance of selecting two purple marbles in a row.
a. To calculate the probability of selecting a purple marble and then a white marble, we multiply the probabilities of each event. The probability of selecting a purple marble on the first draw is 7/9, because there are 7 purple marbles out of 9 marbles total. After removing one marble, there are now 8 marbles left, with 2 white marbles. So, the probability of selecting a white marble on the second draw is 2/8. Multiplying these probabilities, we get (7/9) * (2/8) = 14/72, which simplifies to 7/36.
b. To calculate the probability of selecting two white marbles, we again multiply the probabilities of each event. The probability of selecting a white marble on the first draw is 2/9, since there are 2 white marbles out of 9 marbles total. After removing one marble, there are now 8 marbles left, with 1 white marble. So, the probability of selecting a white marble on the second draw is 1/8. Multiplying these probabilities, we get (2/9) * (1/8) = 2/72, which simplifies to 1/36.
c. Comparing the probabilities from parts a and b, we see that the probability of selecting two white marbles in a row (1/36) is less than the probability of selecting two purple marbles in a row (7/36). Therefore, there is a greater chance of selecting two purple marbles in a row compared to two white marbles in a row.