Question

A bookshelf in a library contains 5 Math books and 15 books of other subjects. If we randomly select two books one after another and without replacement, find the probability of getting 2 math books.

Answer 1

Solution :

Number of Math books = 5

Number of other subjects books = 15

Total number of books = (5 + 15) = 20

Two books are randomly selected one after another and without replacement.

Probability that first selected book is a math book = 5/20

Now, since the book are selected without replacement and one math book is already selected, therefore now we are left with total 19 books in which there are 4 math books.

Hence, probability that second selected book is a math book = 4/19

Using the multiplication theorem of probability we get,

P(getting 2 math books) = (5/20) × (4/19)

P(getting 2 math books) = 1/19

Hence, the probability of getting 2 math books is 1/19.

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