Question

The majors of 700 students at a community college are as follows. 350 boys and 350 girls participated in the survey. 140 boys and 120 girls are majoring in Biology. 100 boys and 100 girls are majoring in Chemistry. 110 boys and 130 girls are majoring in Statistics. Construct a contingency table with this information. Suppose we select a student at random. What is the probability that the student is not a boy? What is the probability that the student is a boy not majoring in stats? What is the probability that the student is a girl given that the major is biology? What is the probability that the student is biology major given that the student is a boy?

Answer 1

1. Probability that the student is not a boy = 0.5

2. Probability that the student is a boy not majoring in Stats = 0.22

3. Probability that the student is a girl given major is Biology = 0.343

4. Probability that the student is a Biology major given the student is a boy = 0.4

Step-by-step explanation:

To begin, construct a contingency table based on the given information, organizing the majors by gender. From this table, the probability that the student is not a boy is calculated by dividing the number of girls by the total number of students, resulting in 0.5.

The probability of a boy not majoring in Stats is found by considering the number of boys not majoring in Stats divided by the total number of students, equating to 0.22.

For the probability that the student is a girl given that the major is Biology, the number of girls majoring in Biology is divided by the total number of Biology majors, arriving at 0.343.

Lastly, to find the probability that the student is a Biology major given that they are a boy, divide the number of boys majoring in Biology by the total number of boys, giving a probability of 0.4. These probabilities are derived from the given data in the contingency table, providing insights into the relationships between gender and major choices among the students at the community college.