08. Suppose a quiz is given that consists of two questions, 60% of the students

Question

08. Suppose a quiz is given that consists of two questions, 60% of the students get the first question correct; 45% get the second question correct, and 30% got both questions correct. A student is chosen at random. Let Ci = the selected student got the 1st question correct C2 the selected student got the 2nd question correct (a) Use probabilities to determine whether C, and C2 are independent. (b) Find the probability that the selected student missed the first question and got the second question correct. (c) Find the probability that given the selected student got the second question correct, they got the first question correct. (d) Find the probability that the selected student got the first question correct or missed the second question.

Explanation / Answer

a)

here P(C1)=0.60 ; P(C2)=0.45 and P(C1 n C2)=0.30

here asP(C1)*P(C2)=0.6*0.45=0.27 which is not equal to  P(C1 n C2)

therefore C1 and C2 are not independent

b)

P(missed fist and get the second question)=P(C2)-P(C1 n C2) =0.45-0.30=0.15

c)

P(first first question correct|second question correct)=P(C1|C2)=P(C1 n C2)/P(C2)

=0.3/0.45 =0.6667

d)

P(C1 U C2c) =1-P(C1c n C2) =1-0.15 =0.85

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