Question

In: Statistics and Probability

In Mr ERIZ’s class, the probability of student who likes Mathematics subject is 0.5 and the...

In Mr ERIZ’s class, the probability of student who likes Mathematics subject is 0.5 and the probability who likes both Mathematics and Statistics subjects is 0.25.

If one student is chosen at random, what is the probability that this student likes Statistics given that he/she also like Mathematics subject?

If the probability of students who like Statistics is 0.45, are the events ‘like Mathematics subject’ and ‘like Statistics subject’ independent? Justify your answer.

(4 marks)

Are the events ‘likes Mathematics’ and ‘likes Statistics’ mutually exclusive? Justify your answer.

Solutions

Expert Solution

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.

Please rate the answer. Thank you.

orchestra answered 1 year ago

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