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01 Jun 2026, 14:45
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E
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Difficulty:
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Question Stats:
76% (01:36) correct
24%
(02:14)
wrong
based on 83
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There are five History and three Science books on a shelf. A student picked three books randomly. What is the probability that he picked at least one Science book?
A. 3/8
B. 5/8
C. 5/28
D. 11/14
E. 23/28
A. 3/8
B. 5/8
C. 5/28
D. 11/14
E. 23/28
01 Jun 2026, 18:05
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\(\mathbb{P}(S \geq 1) \\= 1 - \mathbb{P}(S = 0) \\ = 1- \mathbb{P}(HHH) \\=1-\frac{5}{8}\cdot \frac{4}{7}\cdot \frac{3}{6} \\= 1 - \frac{5}{28} \\= \frac{23}{28} \).
Answer: (E)
Answer: (E)
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01 Jun 2026, 20:07
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Total ways to choose 3 books from 8 books = 8C3 = 56.
The only way to choose no Science books is to choose all 3 books from the 5 History books.
Number of ways = 5C3 = 10.
Therefore, number of ways to choose at least one Science book = 56 − 10 = 46.
Probability = 46/56 = 23/28.
Answer: E
The only way to choose no Science books is to choose all 3 books from the 5 History books.
Number of ways = 5C3 = 10.
Therefore, number of ways to choose at least one Science book = 56 − 10 = 46.
Probability = 46/56 = 23/28.
Answer: E
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