Suppose that a survey of a group of students reveals that 140 are taking computer science only, 62 are taking maths only, 84 are taking both maths and computer science and 27 are taking neither maths nor computer science.What is the probability that a student in this group is taking maths given that they are not taking computer science?
Question
Suppose that a survey of a group of students reveals that 140 are taking computer science only, 62 are taking maths only, 84 are taking both maths and computer science and 27 are taking neither maths nor computer science.What is the probability that a student in this group is taking maths given that they are not taking computer science?
Solution
Step 1: Identify the total number of students
The total number of students is the sum of those taking computer science only, maths only, both maths and computer science, and neither maths nor computer science.
Total students = 140 (computer science only) + 62 (maths only) + 84 (both) + 27 (neither) = 313 students
Step 2: Identify the number of students not taking computer science
The number of students not taking computer science is the sum of those taking maths only and those taking neither maths nor computer science.
Students not taking computer science = 62 (maths only) + 27 (neither) = 89 students
Step 3: Identify the number of students taking maths given that they are not taking computer science
The number of students taking maths given that they are not taking computer science is the number of students taking maths only, since those taking both maths and computer science are excluded.
Students taking maths given not taking computer science = 62 (maths only)
Step 4: Calculate the probability
The probability that a student is taking maths given that they are not taking computer science is the number of students taking maths given not taking computer science divided by the total number of students not taking computer science.
Probability = Students taking maths given not taking computer science / Students not taking computer science
Probability = 62 / 89 = 0.6966 or approximately 0.70 when rounded to two decimal places.
So, the probability that a student in this group is taking maths given that they are not taking computer science is approximately 0.70 or 70%.
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