Mathematics 2000 JAMB Past Questions - Question 45: If U={x:x is an integer and 1 ≤ x ≤ 20} 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

Correct Answer

A

Explanation

U = {1,2,3,4,5,6 +..................+20} Esup1 = {6,9,12,15,18}Esup2 = {4,8,12,16,20}p (picking an integer in Esup2) = 1/4p (not picking an integer in Esup2) = 1- 1/4 = 3/4To find the probability that the randomly chosen integer from the set U is not in E2 (the set of multiples of 4), we need to determine the number of integers in U that are not multiples of 4 and divide it by the total number of integers in U.The set U contains integers from 1 to 20 (inclusive). We can determine the number of integers in U that are multiples of 4 by dividing the largest multiple of 4 (which is 20) by 4 and rounding down to the nearest integer:20 / 4 = 5So, there are 5 integers in U that are multiples of 4.To find the number of integers in U that are not multiples of 4, we subtract the number of multiples of 4 from the total number of integers in U:20 - 5 = 15Therefore, there are 15 integers in U that are not multiples of 4.The probability that the randomly chosen integer from U is not in E2 is given by the ratio of the number of integers in U that are not multiples of 4 to the total number of integers in U:Probability = (Number of integers not in E2) / (Total number of integers in U)Probability = 15 / 20Probability = 3 / 4So, the probability that the randomly chosen integer from U is not in E2 is 3/4 or 0.75.