Question

A bookcase contains 2 statistics books and 5 biology books. if 2 books are chosen at random, the chance that both are statistics books is:________

a. 1/21
b. 10/21
c. 11
d. 21/11

Answer 1

The chance that both are statistics books is
`(1)/(21)`

Explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

`P(A)=(number of favorable cases)/(total number of possible cases)`

Combination of n elements taken from k to k is called each of the ways of choosing k different elements from the n of the original set. That is, it is called combinations of m elements taken from k to k to all the possible groupings that can be made with the m elements. It is expressed as:

`Cn,k=(n!)/(k!*(n-k)!)`

Remember that the factorial of a positive integer n is defined as the product of all the natural numbers before or equal to it.

A bookcase contains 2 statistics books and 5 biology books. The total number of book is 7.

2 books are chosen at random. The total outcomes can be obtained by selection of two books from seven books which is represented as follows:

`C7,2=(7!)/(2!*(7-2)!)=(7!)/(2!*5!)=(5040)/(2*120) =(5040)/(240) =21`

The selection of two statistics book from two statistics book is represented as follows:

`C2,2=(2!)/(2!*(2-2)!)=(2!)/(2!*0!)=(2)/(2*1) =(2)/(2) =1`

Then, the probability is:

`P(A)=(C2,2)/(C7,2)`

`P(A)=(1)/(21)`

The chance that both are statistics books is
`(1)/(21)`