SATHEE: Probability 1 Question 5

Probability 1 Question 5

5. If two different numbers are taken from the set $0, 1 $, $ 2, 3, \dots, 10$ , then the probability that their sum as well as absolute difference are both multiple of 4 , is

(a) $\frac{6}{55}$

(b) $\frac{12}{55}$

(c) $\frac{14}{45}$

(d) $\frac{7}{55}$

(2017 Main)

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Answer:

Correct Answer: 5. (a)

Solution:

Total number of ways of selecting 2 different numbers from $0, 1, 2, \dots, 10 =^{11} C_{2} = 55$

Let two numbers selected be $x$ and $y$ .

$\begin{array}{lc} Then, & x + y = 4 m \\ and & x - y = 4 n \\ \Rightarrow & 2 x = 4 (m + n) and 2 y = 4 (m - n) \\ \Rightarrow & x = 2 (m + n) and y = 2 (m - n) \end{array}$

$∴ x$ and $y$ both are even numbers.

$x$	$y$
0	4,8
2	6,10
4	0,8
6	2,10
8	0,4
10	2,6

$∴$ Required probability $= \frac{6}{55}$

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Probability 1 Question 5

5. If two different numbers are taken from the set 0,1$,$2,3,…,10, then the probability that their sum as well as absolute difference are both multiple of 4 , is

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5. If two different numbers are taken from the set $0, 1 $, $ 2, 3, \dots, 10$ , then the probability that their sum as well as absolute difference are both multiple of 4 , is