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.
1. Pr(p, w)=7/9*2/8
2. pr(w,w)=2/9, 1/8
3. obviously, purple then purple is greatest chance
Pr(p,p)=7/9,6/8
Pr(w,w)=2/9,1/8
THANK YOU!!
To find the probabilities for the given scenarios, we need to determine the total number of possible outcomes and the number of favorable outcomes in each case.
1. Probability of selecting a purple marble and then a white marble:
To find the probability of these two events occurring consecutively, we need to multiply their individual probabilities.
The probability of selecting a purple marble on the first draw is 7 (total number of purple marbles) divided by 9 (total number of marbles in the bag: 2 white + 7 purple), which simplifies to 7/9.
Since the first marble is not replaced, the total number of marbles for the second draw changes. Now there are only 8 marbles in total, with 1 white marble and 7 purple marbles left. Thus, the probability of selecting a white marble on the second draw is 1/8.
To find the probability of both events happening consecutively, we multiply the probabilities:
Probability = (7/9) * (1/8) = 7/72
Therefore, the probability of selecting a purple marble and then a white marble is 7/72.
2. Probability of selecting two white marbles:
To find the probability of selecting two white marbles, we need to consider the individual probabilities for each draw.
The probability of selecting a white marble on the first draw is 2 (total number of white marbles) divided by 9 (total number of marbles in the bag), which simplifies to 2/9.
Since the first marble is not replaced, the total number of marbles decreases for the second draw. Now there is only 1 white marble left out of 8 marbles.
Thus, the probability of selecting a white marble on the second draw is 1/8.
To find the probability of both events happening consecutively, we multiply the probabilities:
Probability = (2/9) * (1/8) = 1/36
Therefore, the probability of selecting two white marbles is 1/36.
3. Comparing the probability of selecting two white marbles in a row and selecting two purple marbles in a row:
The probability of selecting two white marbles in a row is 1/36, as we calculated earlier.
To find the probability of selecting two purple marbles in a row, we need to consider the individual probabilities for each draw:
Probability of selecting a purple marble on the first draw = 7 (total number of purple marbles) divided by 9 (total number of marbles in the bag) = 7/9.
Since the first marble is not replaced, the probability of selecting a purple marble on the second draw is 6 (total number of purple marbles left) divided by 8 (total number of marbles left in the bag) = 6/8 = 3/4.
To find the probability of both events happening consecutively, we multiply the probabilities:
Probability = (7/9) * (3/4) = 21/36
Therefore, the probability of selecting two purple marbles in a row is 21/36, which simplifies to 7/12.
Comparing the probabilities:
The probability of selecting two white marbles in a row (1/36) is lower than the probability of selecting two purple marbles in a row (7/12).
Therefore, there is a greater chance of selecting two purple marbles in a row compared to two white marbles in a row.