If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that:________

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If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that:________

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Tutorconsortium364go Tutorconsortium364go · Answer 1

The probability that:

a dictionary is selected = [tex]\frac{1}{9}[/tex]
two novels and a book of novels is selected = [tex]\frac{5}{14}[/tex]

What is probability?

Probability refers to the possibility of the occurrence of an event.

P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]

Now,

(a) Total number of books = 5 + 3 + 1 = 9

Probability of getting a dictionary = [tex]\frac{1}{9}[/tex]

(b) Number of ways to select 3 books out of 9 books = [tex]\binom{9}{3}[/tex] = [tex]\frac{9!}{3!(6!)} = \frac{9\times\ 8 \times 7}{6}[/tex] = 84

Number of ways to select 1 out of 3 books of poems = [tex]\binom{3}{1} = \frac{3!}{2!}[/tex] = 3

Number of ways to select 2 out of 5 novels = [tex]\binom{5}{2} = \frac{5!}{2! 3!} = \frac{5\times 4}{2} = 10[/tex]

Thus, the probability of getting 2 novels and 1 book of poem = [tex]\frac{3\times10}{84} = \frac{10}{28} = \frac{5}{14}[/tex]

To learn more about probability, refer to the link: https://brainly.com/question/25870256

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(COMPLETE QUESTION:

If three books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) a dictionary is selected? (b) 2 novels and 1 book of poems are selected?)