Two numbers are selected at random from 1, 2, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Total number of ways to select two numbers from $100$ is ${}^{100}C_2 = \frac{100 	imes 99}{2} = 4950$.Let $S$ be the set $\{1, 2, 3, \dots, 100\

Vedclass · Accepted Answer

$0.55$

Vedclass · Answer

(A) Total number of ways to select two numbers from $100$ is ${}^{100}C_2 = \frac{100 	imes 99}{2} = 4950$.Let $S$ be the set $\{1, 2, 3, \dots, 100\}$. The numbers in $S$ divisible by $3$ are $\{3, 6, 9, \dots, 99\}$, which are $33$ in total. The numbers not divisible by $3$ are $100 - 33 = 67$.A product of two numbers is divisible by $3$ if at least one of the selected numbers is divisible by $3$.It is easier to calculate the complement: the product is $NOT$ divisible by $3$ if both selected numbers are $NOT$ divisible by $3$.The number of ways to select two numbers such that neither is divisible by $3$ is ${}^{67}C_2 = \frac{67 	imes 66}{2} = 2211$.The number of ways the product is divisible by $3$ is $4950 - 2211 = 2739$.The required probability is $\frac{2739}{4950} = 0.5533\dots$, which is $0.55$ correct to two decimal places.

Two numbers are selected at random from $1, 2, 3, \dots, 100$ and are multiplied. The probability, correct to two decimal places, that the product thus obtained is divisible by $3$ is:

Similar Questions

An urn contains $9$ red,$7$ white and $4$ black balls. If two balls are drawn at random,then the probability that one is white and the other is red is

$A$ card is drawn at random from a deck of cards. Find the probability of getting the $3$ of diamond.

$A$ card is drawn at random from a pack of $52$ cards. The probability that the drawn card is a court card,i.e.,a jack,a queen,or a king,is

$A$ committee consists of $9$ experts taken from three institutions $A, B$ and $C$,of which $2$ are from $A, 3$ from $B$ and $4$ from $C$. If three experts resign,then the probability that they belong to different institutions is

$A$ word consists of $11$ letters in which there are $7$ consonants and $4$ vowels. If $2$ letters are chosen at random,then the probability that both of them are consonants is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module