A college fds that 8% of students have taken a distance learning class and that

Question

A college fds that 8% of students have taken a distance learning class and that 30% of students are part-time students. Of the part-time students, 20% have taken a distance learning class. Let D-event that a studernt takes a distance learning class and E event that a student is a part-time student. Part (a) Find PID AND E). Part(b) Find PIE I D). Part (c) Find D OR E Part (d) Are D and E independent? Explain. Dand E are dependent events because PD AND E) 05 Dand E are independent events hecause they are mutually exclusive Dand E are independent events because PiDIE) PD) D and E are dependent events because PDIE) PLD Part (e) Are D and E mutually exclusive? Explain O The events are mutually exclusive because they are independent. The events are not mutually exclusive, which means they can be added together and the sum s not 02. The events are not mirtually exclusive because PP AND E) 7 The events are mutually exclusive because HU AND E-0.

Explanation / Answer

1) P(D and E) = P(D|E) * P(E) = 0.2*0.3 = 0.06

2) P(E|D) = P(D and E)/P(D) = 0.06/0.08 = 0.75

3) P(D or E) = P(D) + P(E) - P(D and E) = 0.08 + 0.3 - 0.06 = 0.32

4) Option 4

5) Option 3

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