Question

In a class of 100 half the students are science majors and half are liberal art majors. A student who is a science major has a 0:9 probability of passing a given test whilst a student who is liberal art major has only a probability of 0:7. We pick 2 students at random without replacement and give them the test. What is the probability that both students pass the exam

Answer 1

P(both students passed the exam) = 0.61948

Explanation:

From the given information:

P(both students passed the exam) = P(both are science students or both are art major students or one is from each group)

= P (both are science students) + P(both are art students) + P(one from each group)

where;

P (both are science students) = (50/100) (0.9) × (44/99) × (0.9) = 0.18

P(both students are art) = (50/100) (0.7) × (49/99) 0.7 = 0.1213

P(one of the student are from each group) = (50/100) (0.9) ×(50/99) (0.7) + (50/100) (0.7)× (50/99)(0.9) =0.3182

P(both students passed the exam) = 0.18 + 0.1213 + 0.3182

P(both students passed the exam) = 0.61948