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Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

1. 0.24
2. 0.36
3. 0.4
4. 0.6

on Wednesday we want cs

required probability = $0.6 \times 0.4 + 0.4 \times 0.4 = 0.4$

selected by

prob of studying CS on Tue = 0.4

prob of studying CS on Wed given that it was studied on Tue = 0.4 x 0.4 = 0.16

prob of studying Math on Tue = 0.6

prob of studying CS on Wed given that Math was studied on Tue = 0.6 x 0.4 = 0.24

prob = 0.16 + 0.24 = 0.4
I think both the events are independent events bcoz the prob she studies cs any particular day is .4 and she studies Maths any particular day is  .6 .

Given that she study cs on Mon then,∣

prob(Cs on Wed) = P(Cs on Tue , Cs on Wed) +P(Maths on Tue,Cs on Wed)

=P(Cs on Tue).P(Cs on Wed)+P(Maths on Tue).P(Cs on Wed)

=.4*.4 +.6*.4 =.4

In short, prob(Cs on Wed ∣ Cs on Mon ) = prob(Cs on Wed) = .4      // Independent