In: Statistics and Probability
(4 marks)
Solution :
a) We have following informations :
P(Mathematics) = 0.5
P(Mathematics and Statistics) = 0.25
(i) We have to find P(Statistics | Mathematics).
Hence, the probability that a randomly chosen student likes Statistics given that he/she also like Mathematics subject is 0.5.
ii) Two events A and B are said to be independent iff,
P(A and B) = P(A).P(B)
We have,
P(Mathematics) = 0.5
P(Statistics) = 0.45
P(Mathematics and Statistics) = 0.25
P(Mathematics).P(Statistics) = (0.5 × 0.45) = 0.225
Hence, the events "like Mathematics subject" and "like Statistics subject" are not independent.
iii) Two events A and B are said to be mutually exclusive if
P(A and B) = 0
We have,
P(Mathematics and Statistics) = 0.25 ≠ 0
Hence, the events ‘likes Mathematics’ and ‘likes Statistics’ are not mutually exclusive.
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