Question

Two distinct numbers $x$ and $y$ are chosen from $1,2,3,4,5$. The probability that the arithmetic mean of $x$ and $y$ is an integer is

• A. 0
• B. 1/5
• C. 3/5
• D. 2/5
• E. 4/5

Answer 1

Answer: (D)

Let $S:$ Event that two numberes are selected from $1,2,3,4,5$
$\therefore n(S)={}^5{C}_2=10$
$E:$ Event that two numbers selected have integer mean.
$\therefore E=\{(1,3),(1,5),(2,4),(3,5)\}$
$\therefore n(E)=4$
$\therefore$ Required probability $=P(E)$
$=\frac{n(E)}{n(S)}$
$=\frac{4}{10}$
$=\frac{2}{5}$