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  1. GATE CS
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  3. Engineering Mathematics

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? A. 0.24 B. 0.36 C. 0.4 D. 0.6

GATE 2008 · Engineering Mathematics · Conditional Probability · medium

Answer: P(CS on Wednesday | CS on Monday) = 0.4. Answer: C.

  1. Compute P(Tuesday = CS | Monday = CS): P(CS on Tue | CS on Mon) = 1 - 0.6 = 0.4.
  2. Compute P(Tuesday = Math | Monday = CS): Given directly: if she studies CS on a day, probability of Math next day is 0.6.
  3. Compute P(CS on Wed) via total probability: = (0.4)(0.4) + (0.4)(0.6) = 0.16 + 0.24 = 0.40.