If U = {x : x is an integer and 1 ≤ x ≤ } E1 = {x: x is a multiple of 3} E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the ...
If U = {x : x is an integer and 1 ≤ x ≤ } E1 = {x: x is a multiple of 3} E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2
Answer Details
To find the probability that an integer randomly picked from U is not in E2, we need to find the number of integers in U that are not in E2 and divide it by the total number of integers in U.
First, let's find the number of integers in U that are not in E2. We can do this by finding the complement of E2 in U, which is the set of integers in U that are not in E2. Since E2 is the set of multiples of 4 in U, we can write the complement of E2 as the set of integers in U that are not multiples of 4. We can express this set using set-builder notation as follows:
U \ E2 = {x : x is an integer and x is not a multiple of 4}
To find the number of integers in this set, we can count the number of integers in U that are multiples of 4 and subtract it from the total number of integers in U. The largest integer in U that is a multiple of 4 is 99996, which we can find by dividing 100000 by 4 and taking the floor. Therefore, the number of integers in U that are multiples of 4 is:
floor(100000/4) = 25000
Since U contains all integers from 1 to 100000, the total number of integers in U is:
100000 - 1 + 1 = 100000
Therefore, the number of integers in U that are not in E2 is:
100000 - 25000 = 75000
To find the probability that an integer randomly picked from U is not in E2, we divide the number of integers in U that are not in E2 by the total number of integers in U:
75000/100000 = 0.75
So the probability that an integer randomly picked from U is not in E2 is 0.75 or 75%.
Answer: The correct option is not provided in the question.