5. Use the contingency table below to answer the following questions. Has Cellphones No Cellphones Totals Grade 11 59 6 65 Grade 12 50 3 53 Totals 109 9 118 a. What is the probability that a learner from Grade 11 has a cellphone? b. What is the probability that a learner who does not have a cellphone is from Grade 11? Are the grade of a learner and whether he has a cellphone or not independent events? Explain your answer. C. 6. John and Mary are taking a math course. The course has only 3 grades: A, B, and C. The probability that John gets a B is 0.3. The probability that Mary gets a B is 0.4. The probability that neither gets an A but at least one gets a B is 0.1. What is the probability that at least one gets a B but neither gets a C? 7. Prove that if A and B are independent so are a. A and B b. A and B 8. Suppose that A and B are events such that P(A/B) = P(BA) and P(AUB) = 1 and P( AB) >0. Prove that P(A) > 1/2