7. 60% of Harper students are enrolled full time, 40% of Harper students are enr

Question

7. 60% of Harper students are enrolled full time, 40% of Harper students are enrolled in a math course and 28% are full-time students enrolled in a math course. a. What is the probability

a randomly selected student is full-time or enrolled in a math course?

b. What is the probability a randomly selected student is full-time or enrolled in a math course but not both?

c. What is the probability a randomly selected student is full-time given that the student is enrolled in a math course?

d. Are the events being enrolled full time and being enrolled in a math course independent? Provide statistical justification.

Explanation / Answer

P(full time)=0.6

P(math)=0.4

P(math and full time)=0.28

a) P(math or full time)=P(math)+P(full time)-P(math and full time)=0.6+0.4-0.28=0.72

b) P(math or full time)=0.72 and subtract the P(math and full time) to find the answer . thus it is 0.72-0.28=0.44

c) P(full time | math)= P(math and full time)/P(math)=0.28/0.4=0.7

d) If two events A and B are independent then P(A)*P(B)=P(A and B)

here, P(math)*P(full time)=0.4*0.6=0.24 whereas P(math and full time)=0.28, these are not same so events are not independent

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