State true or false.A lot of 20 books contain 8 books on Mathematics, 5 books on English and the rest are novels. A book is selected at random. The probability that it is a novel is 520.

# State true or false.A lot of 20 books contain 8 books on Mathematics, 5 books on English and the rest are novels. A book is selected at random. The probability that it is a novel is $\frac{5}{20}$.

1. A
True
2. B
False

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### Solution:

Given that the total number of books = 20, number of Mathematics books = 8, and the number of English books = 5.
$n\left(S\right)=20$
Number of novels is calculated by subtracting the sum of the number of Mathematics and English books from the total number of books.
Number of novels = Total number of  books - Number of Mathematics books - Number of English books
$⇒\mathit{Number of novels}=20-8-5$

$⇒n\left(E\right)=7$
We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total possible outcomes n}\left(S\right)}$
Probability that selected book is a novel,
$⇒P\left(E\right)=\frac{7}{20}$
Hence, probability that selected book is a novel is $\frac{7}{20}$.
Therefore, option 2 is correct and the statement is false.

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