Aishwarya studies either computer science or mathematics everyday. If she…
2008
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
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Let C denote computer science and M denote mathematics.
Given P(M next | C today) = 0.6, so P(C next | C today) = 1 - 0.6 = 0.4. Also, P(C next | M today) = 0.4.
Starting from C on Monday, Wednesday can be C through two Tuesday states:
P(C on Wednesday) = P(C on Tuesday and C on Wednesday) + P(M on Tuesday and C on Wednesday)
= P(C on Tuesday | Monday C)P(C on Wednesday | Tuesday C) + P(M on Tuesday | Monday C)P(C on Wednesday | Tuesday M)
= 0.4 x 0.4 + 0.6 x 0.4
= 0.16 + 0.24 = 0.40.
Therefore, the required probability is 0.4.