A college student is taking two courses. The probability she passes the first course is 0.64. The probability she passes the second course is 0.75. The probability she passes at least one of the courses is 0.85. Give your answer to two decimal places. a. What is the probability she passes both courses? Give your answer to two decimal places. b. Is the event she passes one course independent of the event that she passes the other course? True False c. What is the probability she does not pass either course (has two failing grades)? Give your answer to two decimal places. d. What is the probability she does not pass both courses (does not have two passing grades)? Give your answer to two decimal places. e. What is the probability she passes exactly one course? Give your answer to two decimal places

The blue numbers in the attached table of probabilities are given in the problem statement. The purple number is the complement of the given number 0.85. That is, the probability of not passing any is the complement of passing at least 1.

The remaining numbers in the table are the values necessary to make the totals add up. They are obtained by simple subtraction.

(a) p(passing both) = 0.54 . . . . . from the table

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(b) p(passing both) ≠ p(passing 1)×p(passing 2) so they are NOT independent

This is phrased as a question. A question cannot be true or false.

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(c) p(fails both) = 1 - 0.85 = 0.15 . . . . . purple number we filled in the table

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(d) p(does not pass both) = 1 - p(passing both) = 1 - 0.54 = 0.46

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(e) p(passes 1 only) = 0.10 + 0.21 = 0.31