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14.Probability
normal
A number is chosen at random from the set $\{1,2,3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$ . Then the value of $500\ p$ is. . . . . .
A
$210$
B
$214$
C
$220$
D
$225$
(IIT-2021)
Solution
$A=\text { set of numbers divisible by } 3$
$A=\{3,6,9,12, \ldots . . . . . . .1998\}$
$\therefore n(A)=666$
$B=\text { set of numbers divisible by } 7$
$B=\{7,14,21, \ldots .1995\}$
$\therefore n(B)=285$
$A \cap B=\{21,42, \ldots . .1995\}$
$\therefore n(A \cup B)=606+285-95=856$
$\text { required probability }=\frac{856}{2000}=P$
$\text { so, } 500 P=\frac{856}{2000} \times 500=214$
Standard 11
Mathematics
