In a regular 15 -sided polygon with all its diagonals drawn, a diagonal is chosen at random. probabi

English

Gujarati

Hindi

14.Probability

normal

In a regular $15$ -sided polygon with all its diagonals drawn, a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is

A

$\frac{2}{3}$

B

$\frac{5}{6}$

C

$\frac{8}{9}$

D

$\frac{8}{9}$

(KVPY-2020)

Solution

(a)

Total number of diagonals of $15$ sided polygons

$={ }^{15} C_2-15=\frac{15 \times 14}{2}-15=90$

$\therefore$ Number of total shortest digonals $=15$

And number of longest digonals $=15$

$\therefore$ 'he probability that the selected diagonal is neither shortest nor longest

$=\frac{90-30}{90}=\frac{60}{90}=\frac{2}{3}$

Standard 11

Mathematics

Share

Similar Questions

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is

medium

(IIT-2013)

If $m$ rupee coins and $n$ ten paise coins are placed in a line, then the probability that the extreme coins are ten paise coins is

hard

A bag contains $3$ red, $4$ white and $5$ blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is

easy

A bag contains $3$ red, $7$ white and $4$ black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is

medium

If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is

normal