A group of freshmen and sophomore students was selected and each was asked whether they were a member of a student club. The following table was constructed:
Student Club No Student Club
Freshman 4 15
Sophomore 9 7
Find the probability that a randomly selected student form the group is a freshman or is a member of a student club.
Write only a number as your answer. Round to two decimal places (for example: 0.73). Do not write as a percentage.
Frosh = (4+15)/grand total
Member = (4+9)/grand total
Either-or probabilities are found by adding the individual probabilities.
To find the probability that a randomly selected student from the group is a freshman or is a member of a student club, we first need to find the total number of students in the group.
From the table given, we can see that there are 4 freshmen who are members of a student club, 15 freshmen who are not members, 9 sophomores who are members, and 7 sophomores who are not members.
To find the total number of students, we can add up all these values:
Total number of students = 4 (freshmen who are members) + 15 (freshmen who are not members) + 9 (sophomores who are members) + 7 (sophomores who are not members) = 35
Now, to find the probability that a randomly selected student is either a freshman or a member of a student club, we need to add up the number of students who fall into these categories:
Number of students who are either a freshman or a member of a student club = 4 (freshmen who are members) + 9 (sophomores who are members) = 13
Finally, we calculate the probability by dividing the number of students who are either a freshman or a member of a student club by the total number of students:
Probability = Number of students who are either a freshman or a member of a student club / Total number of students = 13 / 35 ≈ 0.37
Therefore, the probability that a randomly selected student from the group is a freshman or is a member of a student club is approximately 0.37.
To find the probability that a randomly selected student is a freshman or is a member of a student club, we need to add the probabilities of these two events occurring.
The total number of students in the group is:
Total number of freshmen + Total number of sophomores = 4 + 9 = 13
The probability of selecting a freshman student is:
Number of freshman students / Total number of students = 4 / 13
The probability of selecting a student who is a member of a student club is:
(Number of freshman students who are members) + (Number of sophomore students who are members)
/ Total number of students = (4 + 9) / 13
Therefore, the probability that a randomly selected student is a freshman or is a member of a student club is:
4/13 + (4 + 9)/13
This can be simplified to:
13/13
So, the probability is 1.