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

Question

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)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let A = 1,2,3, ldots ., 2000 Let E 1=3 m , 1 ≤ m ≤ 666, m ∈ N E 2=7 k , 1 ≤ k ≤ 285, k ∈ N = n ( E 1 ∪ E 2)=666+285-95=856 = P ( E 1 ∪ E 2)=856 / 2000 =500 β=856 / 4=214

Q. A number is chosen at random from the set ${1, 2, 3, \dots .., 2000} .$ 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_____

Let $A = {1, 2, 3, \dots ., 2000}$
Let $E_{1} = 3 m, 1 \leq m \leq 666, m \in N$
$E_{2} = 7 k, 1 \leq k \leq 285, k \in N$
$= n (E_{1} \cup E_{2}) = 666 + 285 - 95 = 856$
$= P (E_{1} \cup E_{2}) = 856/2000$
$= 500 β = 856/4 = 214$

Q. A number is chosen at random from the set {1,2,3,…..,2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7 . Then the value of 500p is_____

Let A={1,2,3,….,2000} Let E1​=3m,1≤m≤666,m∈N E2​=7k,1≤k≤285,k∈N =n(E1​∪E2​)=666+285−95=856 =P(E1​∪E2​)=856/2000 =500β=856/4=214

Q. A number is chosen at random from the set ${1, 2, 3, \dots .., 2000} .$ 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_____

Let $A = {1, 2, 3, \dots ., 2000}$
Let $E_{1} = 3 m, 1 \leq m \leq 666, m \in N$
$E_{2} = 7 k, 1 \leq k \leq 285, k \in N$
$= n (E_{1} \cup E_{2}) = 666 + 285 - 95 = 856$
$= P (E_{1} \cup E_{2}) = 856/2000$
$= 500 β = 856/4 = 214$