Question

Laura has moved to a new apartment. Her schoolbooks comprising of different subjects are mixed in a bag during the move. Four books are of mathematics, three are English, and six are science. If Laura opens the bag and selects books at random, find the given probability.

P(1 science and 2 mathematics books)

Answer 1

Answer:
`(18)/(143)`

Explanation:

Given: The number of Mathematics books = 4

The number of English books =3

The number of science books = 6

Total number of books :
`6+4+3=13`

If Laura opens the bag and selects books at random, then the probability to pick one science book is given by :_

`\text{P(1 science and 2 mathematics books)}=(^6C_1* ^4C_2)/(^(13)C_3)}\\\\\\=(6*(4!)/(2!(4-2)!))/((13!)/(3!(13-3)!))\\\\\\=(6*6)/((13*12*11*10!)/(3!*10!))\\\\\\=(36)/(286)=(18)/(143)`

Hence, the probability to pick one science book is
`(18)/(143)`.

Answer 2

Laura has a total of 13 books. To pick 3 out of this 13 books is expressed as 13C3 which is equal to 286. Now to pick a science and 2 mathematics books may be expressed as,
(4C2) x (6C1) = 36
The probability is the quotient when 36 is dived by 286. The answer is 18/143 which is approximately equal to 0.126.