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..
a. The probability of selecting a purple marble on the first draw is 7/9. Then, there will be only 1 white marble left out of 8 marbles total, so the probability of selecting a white marble on the second draw is 1/8. Therefore, the probability of selecting a purple marble and then a white marble is (7/9) * (1/8) = 7/72.
b. The probability of selecting a white marble on the first draw is 2/9. If a white marble is not replaced, then there will be 1 white marble left out of 8 marbles total, so the probability of selecting a 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. To calculate the probability of selecting two purple marbles in a row, we need to multiply the probability of selecting a purple marble on the first draw (7/9) by the probability of selecting another purple marble on the second draw, given that a purple marble was already selected and not replaced. Since there are now 6 purple marbles and 8 marbles total left, the probability of selecting a purple marble on the second draw is 6/8. Therefore, the probability of selecting two purple marbles in a row is (7/9) * (6/8) = 7/12.
Comparing this to the probability of selecting two white marbles, we see that 1/36 is less than 7/12, so there is a greater chance of selecting two purple marbles in a row than two white marbles in a row.
could you explain with numbers and make it fast and easy?
Sure, here are the probabilities of each event:
a. Probability of selecting a purple marble and then a white marble:
(7/9) * (1/8) = 7/72
b. Probability of selecting two white marbles:
(2/9) * (1/8) = 1/36
c. Probability of selecting two purple marbles in a row:
(7/9) * (6/8) = 7/12
Therefore, there is a greater chance of selecting two purple marbles in a row than two white marbles in a row.
To solve this problem, we need to find the probabilities for each event by applying the concept of conditional probability. Let's go step-by-step:
a. Probability of selecting a purple marble and then a white marble:
First, we calculate the probability of selecting a purple marble. The bag contains a total of 2 white marbles and 7 purple marbles, so the probability of drawing a purple marble on the first draw is 7/9.
Since we don't replace the marble after the first draw, there are now 2 white marbles and a total of 8 marbles left in the bag. Hence, the probability of drawing a white marble on the second draw is 2/8.
To find the probability of both events occurring, we multiply the probabilities together:
P(purple and then white) = P(purple) * P(white after purple)
= (7/9) * (2/8)
= 14/72
= 7/36
Therefore, the probability of selecting a purple marble and then a white marble is 7/36.
b. Probability of selecting two white marbles:
The probability of selecting the first white marble is 2/9.
Since we don't replace the marble after the first draw, there is now only 1 white marble left, and a total of 8 marbles remaining in the bag. Hence, the probability of drawing the second white marble is 1/8.
To find the probability of both events occurring, we multiply the probabilities together:
P(white and then white) = P(white) * P(white after white)
= (2/9) * (1/8)
= 2/72
= 1/36
Therefore, the probability of selecting two white marbles is 1/36.
c. Comparing the chances of selecting two white marbles in a row and two purple marbles in a row:
From the previous calculations, we found that the probability of selecting two white marbles in a row is 1/36, and the probability of selecting two purple marbles in a row is 7/36.
Since 1/36 is less than 7/36, there is a greater chance of selecting two purple marbles in a row compared to two white marbles in a row.