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

Answer:

The chance that both are statistics books is $\frac{1}{21}$

Step-by-step 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.

$P(A)=\frac{number of favorable cases}{total number of possible cases}$

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:

$Cn,k=\frac{n!}{k!*(n-k)!}$

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:

$C7,2=\frac{7!}{2!*(7-2)!}=\frac{7!}{2!*5!}=\frac{5040}{2*120} =\frac{5040}{240} =21$

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

$C2,2=\frac{2!}{2!*(2-2)!}=\frac{2!}{2!*0!}=\frac{2}{2*1} =\frac{2}{2} =1$

Then, the probability is:

$P(A)=\frac{C2,2}{C7,2}$

$P(A)=\frac{1}{21}$

The chance that both are statistics books is $\frac{1}{21}$