Two integers are drawn at random from the set | vedclass

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(D) The set is $S = \{5, 6, \ldots, 35\}$. The number of elements is $35 - 5 + 1 = 31$.The total number of ways to choose $2$ integers from $31$ is $^

Vedclass · Accepted Answer

$\frac{16}{31}$

Vedclass · Answer

(D) The set is $S = \{5, 6, \ldots, 35\}$. The number of elements is $35 - 5 + 1 = 31$.The total number of ways to choose $2$ integers from $31$ is $^{31}C_2 = \frac{31 	imes 30}{2} = 465$.The difference between two integers is odd if and only if one integer is even and the other is odd.In the set $\{5, 6, \ldots, 35\}$,the number of odd integers is $16$ (i.e.,$5, 7, \ldots, 35$) and the number of even integers is $15$ (i.e.,$6, 8, \ldots, 34$).The number of ways to choose one odd and one even integer is $^{16}C_1 	imes ^{15}C_1 = 16 	imes 15 = 240$.The probability that the difference is odd is $P = \frac{240}{465}$.Dividing both numerator and denominator by $15$,we get $P = \frac{16}{31}$.

Two integers are drawn at random from the set $\{5, 6, \ldots, 35\}$. What is the probability that their difference is odd?

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