Consider the experiment of rolling a die. Let A be the event 'getting a prime number', B be the event 'getting an odd number'. However C be the event containing only highest number of die. If P is the probability of the events.
(A) Here, \(S=\{1,2,3,4,5,6\}\), \(A=\{2,3,5\}\), \(B=\{1,3,5\}\), \(C=\{6\}\)
(B) \(A\cup B=\{1,2,3,5\}\) & \(A\cap B=\{3,5\}\)
(C) \(P(A)\geq 0\), \(P(B)\geq 0\), \(P(C)\geq 0\)
(D) \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
Arrange the above events in chronological order and choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B), (C), (D)
The four lines are the steps of working with these events, and each step needs the one before it. Their order is therefore the order in which the working is done:
(A) first: the sample space S and the events A, B, C are listed, since nothing can be combined or measured before the outcomes are known.
(B) next: the union and the intersection of A and B are formed from the sets written in (A).
(C) then: the probabilities of the events are taken, starting from the basic rule that a probability is never negative.
(D) last: the addition rule \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) uses the union and intersection of (B) and the probabilities of (C).