In class of 125 students, 70 students passed in Math, 56 students passed in Statistics, and 30 passed in both. The probability that a student selected at random from the class, has passed in only one subject is
Draw a Venn diagram or use the inclusion/exclusion principle to show that
there are 70-30=40 students passed only math, and 56-30=26 students passed only statistics.
So there is a total of 40+26=66 students who passed only one subject.
So what is the probability of randomly choosing one student from a class of 125 such that this student is one of 66 who passed only one subject?
u6
To find the probability that a student selected at random from the class has passed in only one subject, we need to calculate the number of students who have passed in exactly one subject.
Let's break down the problem:
- Total number of students in the class: 125
- Number of students who passed in Math: 70
- Number of students who passed in Statistics: 56
- Number of students who passed in both subjects: 30
To find the number of students who passed in only one subject, we need to subtract the number of students who passed in both subjects from the total number of students who passed in each subject individually.
Number of students who passed in only Math = Number of students who passed in Math - Number of students who passed in both subjects = 70 - 30 = 40
Number of students who passed in only Statistics = Number of students who passed in Statistics - Number of students who passed in both subjects = 56 - 30 = 26
Now, we can calculate the probability that a student selected at random from the class has passed in only one subject by dividing the number of students who passed in only one subject by the total number of students in the class.
Probability = (Number of students who passed in only one subject) / (Total number of students in the class) = (40 + 26) / 125 = 66 / 125
Therefore, the probability that a student selected at random from the class has passed in only one subject is 66/125.