There are four sections of Probability, with section I having 40 students, secti

Question

There are four sections of Probability, with section I having 40 students, section II having 60 students, section III having 70 students, section IV having 30 students.

• The probability of getting an A in section I is 0.2.

• The probability of getting an A in section II is 0.1.

• The probability of getting an A in section III is 0.3.

• The probability of getting an A in section IV is 0.05.

If someone told you that she was in one of the four sections, and that she got an A, what is the probability that

(a) she was in section I?

(b) she was in section II?

(c) she was in section III?

(d) she was in section IV?

Explanation / Answer

Total number of students = 40+60+70+30 = 200

P(getting an A) = (40/200)x0.2 + (60/200)x0.1 + (70/200)x0.3 + (30/200)x0.05

= 0.1825

(a) P(section I | got an A) = P(getting A and section I) / P(getting an A)

= (40/200)x0.2 / 0.1825

= 0.2192

(b) P(section II | got an A) = P(getting A and section II) / P(getting an A)

= (60/200)x0.1 / 0.1825

= 0.1644

(c) P(section III | got an A) = P(getting A and section III) / P(getting an A)

= (70/200)x0.3 / 0.1825

= 0.5753

(d) P(section IV | got an A) = P(getting A and section IV) / P(getting an A)

= (30/200)x0.05 / 0.1825

= 0.0411

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