In a group of students, 10 like mathematics, 8 like science, and 5 like both subjects. If a student is chosen randomly, what is the probability that the student likes only mathematics? a. 2/10 b. 7/13 c. 5/13 d. 6/10
Question
In a group of students, 10 like mathematics, 8 like science, and 5 like both subjects. If a student is chosen randomly, what is the probability that the student likes only mathematics? a. 2/10 b. 7/13 c. 5/13 d. 6/10
Solution
To solve this problem, we first need to determine the total number of students and the number of students who only like mathematics.
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Determine the total number of students: The problem states that 10 students like mathematics, 8 like science, and 5 like both. So, the total number of students is the number of students who like mathematics plus the number of students who like science, minus the number of students who like both (since they were counted twice). This gives us 10 + 8 - 5 = 13 students.
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Determine the number of students who only like mathematics: The problem states that 10 students like mathematics and 5 students like both mathematics and science. So, the number of students who only like mathematics is the number of students who like mathematics minus the number of students who like both. This gives us 10 - 5 = 5 students.
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Calculate the probability: The probability that a student chosen at random likes only mathematics is the number of students who only like mathematics divided by the total number of students. This gives us 5 / 13.
So, the correct answer is c. 5/13.
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