Three integers are chosen at random from the | vedclass

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

Question

(C) The total number of ways to choose $3$ integers from the first $20$ integers is $^{20}C_3 = \frac{20 	imes 19 	imes 18}{3 	imes 2 	imes 1} = 1

Vedclass · Accepted Answer

$\frac{17}{19}$

Vedclass · Answer

(C) The total number of ways to choose $3$ integers from the first $20$ integers is $^{20}C_3 = \frac{20 	imes 19 	imes 18}{3 	imes 2 	imes 1} = 1140$.The product of three integers is even if at least one of the chosen integers is even.It is easier to calculate the probability that the product is odd. The product is odd if and only if all three chosen integers are odd.There are $10$ odd integers and $10$ even integers in the first $20$ integers.The number of ways to choose $3$ odd integers is $^{10}C_3 = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$.The probability that the product is odd is $P(	ext{odd}) = \frac{^{10}C_3}{^{20}C_3} = \frac{120}{1140} = \frac{12}{114} = \frac{2}{19}$.The probability that the product is even is $P(	ext{even}) = 1 - P(	ext{odd}) = 1 - \frac{2}{19} = \frac{17}{19}$.

Three integers are chosen at random from the first $20$ integers. The probability that their product is even,is

Similar Questions

There are $6$ positive and $8$ negative numbers. If four numbers are chosen at random and multiplied,the probability that the product is a negative number is

Three numbers are chosen at random from numbers $1$ to $20$. The probability that they are consecutive is

Out of $21$ tickets marked with numbers from $1$ to $21$,three are drawn at random. The chance that the numbers on them are in $A.P.$ is

$A$ bag contains $6$ white and $4$ black balls. Two balls are drawn at random. The probability that they are of the same colour is . . . . . .

Three squares of a chessboard are chosen at random. The probability that two are of one colour and one is of another colour is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module