Let \( S=\{1,2,3, \ldots \ldots n\} \) be a set and two numbers \( x \) and \( y \) are drawn wi... VIDEO
Let \( S=\{1,2,3, \ldots \ldots n\} \) be a set and two numbers \( x \) and \( y \) are drawn with replacement from \( S \). Let \( P_{2} \) be the probability that \( x^{2}-y^{2} \) is divisible by \( 2 \&[\cdot] \) denotes greatest integer less than or equal to \( x \).
The value of \( \mathrm{P} 2 \) is equal to
(a) \( \frac{1}{2} \)
(b) \( \left(\frac{\left[\frac{n}{2}\right]}{n}\right)^{2} \)
(c) \( 1-2 . \frac{\left[\frac{n}{2}\right]}{n}+2\left(\frac{\left[\frac{n}{2}\right]}{n}\right)^{2} \)
(d) \( 1-\frac{2-\left[\frac{n}{2}\right]}{n}-2\left(\frac{\left[\frac{n}{2}\right]}{n}\right)^{2} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-06-09 \( P(A)=\frac{3}{8} ; P(B)=\frac{1}{2} ; P(A \cup B)=\frac{5}{8} \), which of the following do/d... 2023-06-09 Three balls are randomly and independantly tossed into bins numbered with the positive integers ... 2023-06-09 If \( E_{1} \) and \( E_{2} \) are two events such that \( P\left(E_{1}\right)=1 / 4, P\left(E_{... 2023-06-09 An unbiased coin is tossed \( \mathrm{n} \) times. Let \( X \) denote the number of times head o... 2023-06-09 A pair of fair dice having six faces numbered from 1 to 6 are thrown once, suppose two events \(... 2023-06-09 Three numebrs are selected simultaneously from the set \( \{1,2,3, \ldots, 25\} \). The probabil... 2023-06-09 Jerry starts at 0 on the real number line. He tosses a fair coin 8 times. When he gets heads, he... 2023-06-09 Alex, Mel and Chelsea play a game that has 6 rounds. In each round there is a single winner, and... 2023-06-09 If \( X \) follows a binomial distribution with parameters \( n=8 \) and \( P \) is \( 1 / 2 \),... 2023-06-09 A positive integer divisor of 12 ! is chosen at random. The probability that the division chosen... 2023-06-09 Let \( S=\{1,2,3, \ldots \ldots n\} \) be a set and two numbers \( x \) and \( y \) are drawn wi... 2023-06-09 A drawer contains 6 brown and 8 black socks well mixed. A man reaches the drawer and pulls out s... 2023-06-09 16 players take part in a tennis tournament. The order of the matches is chosen at random. There... 2023-06-09 Una rolls 6 standard 6-sided dice simultaneously and calculates the product of the 6 numbers obt... 2023-06-09 The numbers \( 1,2, \ldots, 9 \) are randomly placed into the 9 squares of a \( 3 \times 3 \) gr... 2023-06-09 If \( p, q \) and \( r \) are three numebrs (not necessarily different) chosen randomly and with... 2023-06-09 To maintain his health a person must fulfil certain minimum daily requirements for several kinds... 2023-06-09 Three fair dice are rolled once. Given that atleast one of them shows up the face 6 . The chance... 2023-06-09 A man alternatively tosses a fair coin and rolls a fair ordinary dice. He starts with the coin. ... 2023-06-09 A covered basket of flowers has some lilies and roses. In search of rose, Sweety and Shweta alte... 2023-06-09 A bag contains 4 red, 5 white and 6 black balls. Three balls are selected from this bag simultan...