An integer is chosen at random and squared. T | vedclass

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

Question

(B) The last digit of the square of an integer depends only on the last digit of the integer itself.Let the last digit of the integer be $x$,where $x

Vedclass · Accepted Answer

$\frac{3}{10}$

Vedclass · Answer

(B) The last digit of the square of an integer depends only on the last digit of the integer itself.Let the last digit of the integer be $x$,where $x \in \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$.The squares of these digits are:$0^2 = 0$$1^2 = 1$$2^2 = 4$$3^2 = 9$$4^2 = 16$ (last digit $6$)$5^2 = 25$ (last digit $5$)$6^2 = 36$ (last digit $6$)$7^2 = 49$ (last digit $9$)$8^2 = 64$ (last digit $4$)$9^2 = 81$ (last digit $1$)The last digits of the squares are $\{0, 1, 4, 9, 6, 5, 6, 9, 4, 1\}$.We want the last digit of the square to be $1$ or $5$.The cases where the last digit is $1$ are $x = 1$ and $x = 9$ (total $2$ cases).The case where the last digit is $5$ is $x = 5$ (total $1$ case).Total favorable outcomes = $2 + 1 = 3$.Total possible outcomes = $10$.Therefore,the required probability = $\frac{3}{10}$.

$Face$	$1$	$2$	$3$	$4$	$5$	$6$
$Probability$	$0.2$	$0.22$	$0.11$	$0.25$	$0.05$	$0.17$

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

Similar Questions

When two dice are thrown simultaneously,what is the probability that the numbers appeared on both dice are equal?

The probability that a leap year selected randomly will have $53$ Sundays is

There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is

For a biased die,the probabilities for different faces to turn up are

$Face$ $1$ $2$ $3$ $4$ $5$ $6$

$Probability$ $0.2$ $0.22$ $0.11$ $0.25$ $0.05$ $0.17$

The die is tossed and you are told that either face $4$ or face $5$ has turned up. The probability that it is face $4$ is

The probability of getting a sum of $16$ in one throw with three dice is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module