If four vertices a regular octagon are c...

If four vertices a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is

A

`(1)/(8)`

B

`(2)/(21)`

C

`(1)/(32)`

D

`(1)/(35)`

Text Solution

Verified by Experts

The correct Answer is:

D

`(d)` As shown in figure here, four rectangles are formed.
`:.` Number of favourable cases `=4`
and total number of cases `=^(8)C_(4)`
`:.` Required probability
`=(4)/("^(9)C_(4))=(2)/(35)`

Topper's Solved these Questions

PRINCIPLE OF MATHEMATICAL INDUCTION
CENGAGE PUBLICATION|Exercise Sovled Examples|22 Videos
PROBABILITY I
CENGAGE PUBLICATION|Exercise JEE Advanced|7 Videos

Similar Questions

Explore conceptually related problems

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is (a) 1/2 (b) 1/5 (c) 1/10 (d) 1/20

If out of 20 consecutive whole numbers two are chosen at random, then find the probability that their sum is odd.

Two integers are chosen at random and multiplied. Find the probability that the product is an even integer.

An integer is chosen at random and squared. Find the probability that the last digit of the square is 1 or 5.

If 30 dates are named at random,find the probability that 5 of them will be sundays.

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, then find the probability that it is rusted or is a nail.

There are four letters and four envelopes bearing addresses at random. The probability that the letters are placed in correct envelopes is (K)/(24) , then find the value of K.

If 30 dates are named at random, what is the probability that 5 of them will be Sundays?

If 16 dates are named at random , what is the probability that 3 of them will be Sunday?

Out of 30 consecutive natural numbers, 2 are chosen at random. The probability that their sum is odd is -

CENGAGE PUBLICATION-PROBABILITY-All Questions

Which of the following statement is/are correct? (a)Three coins are t...
Text Solution
|
The probability that a 50-years-old man will be alive at 60 is 0.83 an...
Text Solution
|
If four vertices a regular octagon are chosen at random, then the prob...
Text Solution
|
Six fair dice are thrown independently. The probability that three are...
Text Solution
|
If the letters of the word MATHEMATICS are arranged arbitrarily, the p...
Text Solution
|
Two squares of 1xx1 are chosen at random on a chestboard. What is the ...
Text Solution
|
In a game of chance a player throws a pair of dice and scores points e...
Text Solution
|
If a and b are randomly chosen from the set {1,2,3,4,5,6,7,8,9}, then ...
Text Solution
|
A word of at least 5 letters is made at random from 3 vowels and 3 con...
Text Solution
|
Matrices of order 3xx3 are formed by using the elements of the set A={...
Text Solution
|
A box contains 10 tickets numbered from 1 to 10 . Two tickets are draw...
Text Solution
|
Three vertices are chosen randomly from the seven vertices of a regula...
Text Solution
|
Given four pair of gloves, they are distributed to four persons. Each ...
Text Solution
|
The probability that sin^(-1)(sinx)+cos^(-1)(cosy) is an integer x,y i...
Text Solution
|
Of all the mappings that can be defined from the set A :{1,2,3,4} to B...
Text Solution
|
Five different marbles are placed in 5 different boxes randomly. Then ...
Text Solution
|
10 different books and 2 different pens are given to 3 boys so that ea...
Text Solution
|
Let a function f : XtoY is defined where X={0,1,2,3,….,9}, Y={0,1,2,…....
Text Solution
|
If two distinct numbers m and n are chosen at random form the set {1, ...
Text Solution
|
Given that x in [0,1] and y in [0,1]. Let A be the event of selecting ...
Text Solution
|