The table shows the numbers of students at a college who study maths or not. | Study Maths | Male | Female | |----------------------|------|--------| | Do Not Study Maths | 110 | 90 | | Study Maths | 130 | 170 | a) A student is selected at random. Find the probability that i) the student is male; ii) the student is a female who studies maths; iii) the student is a male, given that they study maths.
Answer (1)
To solve this problem, we need to analyze the probability of selecting a student based on the given conditions. Let's break this down step by step.
First, we will summarize the given data into a table format:
Students who do not study Maths:
Male: 110
Female: 90
Students who study Maths:
Male: 130
Female: 170
Next, we'll calculate the total number of students in each category.
Total Students:
Total Students = (Total Male) + (Total Female)
Total Male = 110 (Do Not Study Maths) + 130 (Study Maths) = 240
Total Female = 90 (Do Not Study Maths) + 170 (Study Maths) = 260
Total Students = 240 + 260 = 500
a) Find the probability:
i) Probability that the student is male: The total number of male students is 240.
P ( male ) = Total Students Total Male = 500 240 = 0.48
ii) Probability that the student is a female who studies maths: There are 170 female students who study maths.
P ( female and studies maths ) = 500 170 = 0.34
iii) Probability that the student is male, given that they study maths: First, find the total number of students who study maths: 130 males + 170 females = 300.
P ( male ∣ study maths ) = Total Students who Study Maths Number of Males who Study Maths = 300 130 = 30 13 ≈ 0.4333
In summary, the probabilities are:
Probability that a student is male: 0.48
Probability that a student is a female who studies maths: 0.34
Probability that a student is male, given that they study maths: approximately 0.4333.
Each of these probabilities is calculated with reference to the total student body or the respective subgroup specified in the question.
