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27 Nov 2020, 08:06
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At least one grey scarf: \(\frac{17}{24}\)
Exactly two grey scarves: \(\frac{7}{40}\)
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
71% (02:06) correct
29%
(01:27)
wrong
based on 7
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Not Attempted Yet
Every New Year's Eve, Pratik gives scarves as gifts to his coworkers. This year, to show his appreciation, he asks Malachi to be the first to choose three scarves. To make it more fun, Malachi must pick three scarves blindly from a box containing 10 scarves.
The box holds 3 grey, 4 white, 2 yellow, and 1 black scarf. In the table, select one value for the probability that Malachi picks at least one grey scarf and another for the probability of picking exactly two grey scarves. Make only two selections, one in each column.
The box holds 3 grey, 4 white, 2 yellow, and 1 black scarf. In the table, select one value for the probability that Malachi picks at least one grey scarf and another for the probability of picking exactly two grey scarves. Make only two selections, one in each column.
| At least one grey scarf | Exactly two grey scarves | |
| \(\frac{1}{720}\) | ||
| \(\frac{7}{720}\) | ||
| \(\frac{7}{40}\) | ||
| \(\frac{7}{24}\) | ||
| \(\frac{1}{2}\) | ||
| \(\frac{17}{24}\) |
ShowHide Answer
Official Answer
At least one grey scarf: \(\frac{17}{24}\)
Exactly two grey scarves: \(\frac{7}{40}\)
27 Nov 2020, 08:06
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Official Solution:
To find the probability of Malachi picking at least one grey scarf, let's calculate the probability of the opposite event and subtract it from 1. The opposite event is selecting zero grey scarves, meaning choosing all three scarves from the 4 white, 2 yellow, and 1 black scarf. Therefore, the probability is \(P(at \ least \ one \ grey \ scarf) = 1 - \frac{C^3_7}{C^3_{10}}= 1 - \frac{35}{120} = \frac{17}{24}\).
Alternatively, we could have used a probability approach in the last step: \(P(at \ least \ one \ grey \ scarf) = 1 - \frac{7}{10} * \frac{6}{9} * \frac{5}{8} = \frac{17}{24}\).
To find the probability of Malachi picking exactly two grey scarves, we calculate the probability of selecting two grey scarves and one scarf from the 7 non-grey scarves: \(P(exactly \ two \ grey \ scarves) = \frac{C^2_3 * C^1_7}{C^3_{10}}= \frac{3 * 7}{120} = \frac{7}{40}\).
Correct answer:
At least one grey scarf "\(\frac{17}{24}\)"
Exactly two grey scarves "\(\frac{7}{40}\)"
Bunuel
Every New Year's Eve, Pratik gives scarves as gifts to his coworkers. This year, to show his appreciation, he asks Malachi to be the first to choose three scarves. To make it more fun, Malachi must pick three scarves blindly from a box containing 10 scarves.
The box holds 3 grey, 4 white, 2 yellow, and 1 black scarf. In the table, select one value for the probability that Malachi picks at least one grey scarf and another for the probability of picking exactly two grey scarves. Make only two selections, one in each column.
The box holds 3 grey, 4 white, 2 yellow, and 1 black scarf. In the table, select one value for the probability that Malachi picks at least one grey scarf and another for the probability of picking exactly two grey scarves. Make only two selections, one in each column.
| At least one grey scarf | Exactly two grey scarves | |
| \(\frac{1}{720}\) | ||
| \(\frac{7}{720}\) | ||
| \(\frac{7}{40}\) | ||
| \(\frac{7}{24}\) | ||
| \(\frac{1}{2}\) | ||
| \(\frac{17}{24}\) |
To find the probability of Malachi picking at least one grey scarf, let's calculate the probability of the opposite event and subtract it from 1. The opposite event is selecting zero grey scarves, meaning choosing all three scarves from the 4 white, 2 yellow, and 1 black scarf. Therefore, the probability is \(P(at \ least \ one \ grey \ scarf) = 1 - \frac{C^3_7}{C^3_{10}}= 1 - \frac{35}{120} = \frac{17}{24}\).
Alternatively, we could have used a probability approach in the last step: \(P(at \ least \ one \ grey \ scarf) = 1 - \frac{7}{10} * \frac{6}{9} * \frac{5}{8} = \frac{17}{24}\).
To find the probability of Malachi picking exactly two grey scarves, we calculate the probability of selecting two grey scarves and one scarf from the 7 non-grey scarves: \(P(exactly \ two \ grey \ scarves) = \frac{C^2_3 * C^1_7}{C^3_{10}}= \frac{3 * 7}{120} = \frac{7}{40}\).
Correct answer:
At least one grey scarf "\(\frac{17}{24}\)"
Exactly two grey scarves "\(\frac{7}{40}\)"
15 Nov 2024, 07:14
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I have revised the question, solution, and formatting by adding more details to enhance clarity
