Question

Let the sample space for an experiment be {1, 2, 3, 5, 8, 13, 21}. Assume you pull one number at random from the sample space.

Let A be the event the number pulled is odd

Let B be the event the number pulled is greater than 7

What is the probability of event A occurring.

What is the probability of B not occuring?

What is the probability of A and B occuring?

What is the probability of A or B occuring?

Is B a subset of A?

Answer 1

a) The probability of event A occurring is computed here as:

P(A) = P(number pulled is odd) = 5/7

Therefore 5/7 is the required probability here.

b) The probability of B not occurring is computed here as:

= 1 - P(number pulled is greater than 7)

= 1 - (3/7)

= 4/7

Therefore 4/7 is the required probability here.

c) P(A and B) = P(odd and greater than 7)

= 2/7 as there are only 2 such numbers: 13 and 21

Therefore 2/7 is the required probability here.

d) P(A or B) = P(A) + P(B) - P(A and B)

= (5/7) + (3/7) - (2/7) = 1

Therefore (6/7) is the required probability here.

e) All the elements of B: 8, 21 and 13 are not there in A, that is 8 is not in A.

Therefore no B is not a subset of A.