Please check my answers!
A(A box contains 2 yellow,3 red,2 blue,3 purple, and 4 pink marbles.Once a marble is selected, it is {{not}} replaced. Find each probability.
1.P(two purple marbles)
my answer~ 1/91
2. P(two yellow marbles)
my answer~ 2/4 or 1/7
These next ones I need help on the most..
3. P(pink marbles then a red marble)
my answer~1/72
4.P(two marbles that are {{not}} blue)
my answer~2/8
5.P(two marbles that are neither yellow nor pink)
my answer~2/5
#1. 3/14 * 2/13 = 3/91
#2. 2/14 * 1/13 = 1/91
#3. 4/14 * 3/13 = 6/91
#4. 12/14 * 11/13 = 66/91
#5. 8/14 * 7/13 = 28/91
Let's go through each question and calculate the probabilities step by step.
1. P(two purple marbles):
To find the probability of selecting two purple marbles from the box without replacement, you need to calculate the number of favorable outcomes divided by the total number of possible outcomes. In this case, there are 3 purple marbles in the box, so the probability of selecting one purple marble on the first draw is 3/14. After removing one purple marble from the box, there are 2 purple marbles left out of a total of 13 marbles. So the probability of selecting another purple marble on the second draw is 2/13. To find the probability of both events happening, multiply the individual probabilities: (3/14) * (2/13) = 6/182 = 3/91. Thus, the correct answer is 3/91.
2. P(two yellow marbles):
Similarly, to find the probability of selecting two yellow marbles without replacement, you need to calculate the probability of selecting one yellow marble on the first draw and another on the second draw. There are 2 yellow marbles in the box, so the probability of selecting one yellow marble on the first draw is 2/14. After removing one yellow marble, there is 1 yellow marble left out of a total of 13 marbles. So the probability of selecting another yellow marble on the second draw is 1/13. To find the probability of both events happening, multiply the individual probabilities: (2/14) * (1/13) = 2/182 = 1/91. Thus, the correct answer is 1/91.
3. P(pink marbles then a red marble):
To find the probability of selecting a pink marble first and then a red marble without replacement, you need to calculate the probability of selecting one pink marble on the first draw and then one red marble on the second draw. There are 4 pink marbles in the box, so the probability of selecting a pink marble on the first draw is 4/14. After removing one marble, there are 3 red marbles left out of a total of 13 marbles. So the probability of selecting a red marble on the second draw is 3/13. To find the probability of both events happening, multiply the individual probabilities: (4/14) * (3/13) = 12/182 = 6/91. Thus, the correct answer is 6/91.
4. P(two marbles that are not blue):
To find the probability of selecting two marbles that are not blue without replacement, you need to calculate the probability of not selecting a blue marble on both the first and second draws. There are 9 marbles that are not blue in the box, so the probability of not selecting a blue marble on the first draw is 9/14. After removing one marble, there are 8 marbles that are not blue left out of a total of 13 marbles. So the probability of not selecting a blue marble on the second draw is 8/13. To find the probability of both events happening, multiply the individual probabilities: (9/14) * (8/13) = 72/182 = 36/91. Thus, the correct answer is 36/91.
5. P(two marbles that are neither yellow nor pink):
To find the probability of selecting two marbles that are neither yellow nor pink without replacement, you need to calculate the probability of not selecting a yellow or pink marble on both the first and second draws. There are 7 marbles in the box that are neither yellow nor pink, so the probability of not selecting a yellow or pink marble on the first draw is 7/14. After removing one marble, there are 6 marbles left that are neither yellow nor pink out of a total of 13 marbles. So the probability of not selecting a yellow or pink marble on the second draw is 6/13. To find the probability of both events happening, multiply the individual probabilities: (7/14) * (6/13) = 42/182 = 21/91. Thus, the correct answer is 21/91.
I hope this clarifies the correct probabilities for each question.