Question

1. A country club has a membership of 500 members and operates facilities that include a swimming pool and a gymnasium. The club president would like to know how many members regularly use the facilities. A survey of the members indicates that 70% regularly use the swimming pool (S), 50% regularly use the gymnasium (G), and 5% use neither of these facilities regularly. Calculate the probability of the club members who use the facilities of the swimming pool and gymnasium P(S∩G).           

                    

2. 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.

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

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

(4 marks)

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

Answer 1

Solution :

a) We have following informations :

P(S) = 70% = 0.70

P(G) = 50% = 0.50

We have to find P(S ∩ G).

P(S ∩ G) = P(S) + P(G) - P(S ∪ G)

b) 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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