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

Answer 1

The answer is 1/15.
number of ways to choose any 2 books out of 5 biology books =⁵C₂ = 5!(2! x 3!) =10
number of ways to choose 2 statistic books out of 2 = ²C₂ = 1
So, probability that both two books are statistics books = 1/10

Answer 2

The chance that both the book are of statistics is $\boxed{\dfrac{1}{21}}$.

Further Explanation:

Given:

The total number of statistics book is $2$.

The total number of biology book is $5$.

Concept used:

Probability is defined as the ratio of favorable outcomes to total outcomes.

$\boxed{\text{Probability}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}}$.

Combination is defined as the selection of all or part of object without considering the order of the object.

$\boxed{^{n}C_{r}=\dfrac{n!}{r!\cdot (n-r)!}}$

Here, $n$ is the total number of object and $r$ is the number of object to be chosen.

Calculation:

The total number of book is $7$.

The chance of getting the statistics books is the favorable outcomes for the problem.

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

$\boxed{^{2}C_{2}}$

The total outcomes can be obtained by selection of two books from seven books which is represented as follows:

$\boxed{^{7}C_{2}}$

Write the formula to obtain the chance that both the books are statistics.

$\boxed{P=\dfrac{^{2}C_{2}}{^{7}C_{2}}}$

Solve the above equation to obtain the chance that both the books are of statistics.

$\begin{aligned}P&=\dfrac{^{2}C_{2}}{^{7}C_{2}}\\&=\dfrac{\frac{2!}{2!\cdot (2-2)!}}{\frac{7!}{2!\cdot (7-5)!}}\\&=\dfrac{1}{\frac{7\times 6}{2}}\\&=\dfrac{1}{21}\end{aligned}$

Therefore, the probability that the two selected books are of statistics is $\boxed{\dfrac{1}{21}}$.

Learn more:

1. Simplification: https://brainly.com/question/1602237

2. Quadratic equation: https://brainly.com/question/1332667

Answer details:

Grade: High school.

Subject: Mathematics.

Chapter: Probability.

Keywords: Probability, statistics, favorable, outcomes, total outcomes, 0.047, \frac{1}{{21}}, chance, biology books, 2, 7,  chances, randomly chosen.