Sample Space:
When a die is rolled,
S = {1, 2, 3, 4, 5, 6}
Given Events:
E: Die shows 4
E = {4}
F: Die shows an even number
F = {2, 4, 6}
Check for mutual exclusiveness:
E ∩ F = {4}
Since E ∩ F ≠ ∅,
E and F are not mutually exclusive.
Final Answer:
The events E and F are not mutually exclusive.
A die is thrown. Describe the following events:
(i) \(A: a\) number less than \(7\)
(ii) \(B: a\) number greater than \(7\)
(iii) \(C: a\) multiple of \(3\)
(iv) \(D: a\) number less than \(4\)
(v) \(E: a\) even number greater than \(4\)
(vi) \(F: a\) number not less than \(\)\(3\)
Also, find \(A∪B, A∩B, B∪C, E∩F, D∩E, A-C, D-E, E∩F', F'\)
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: \(A:\) the sum is greater than \(8\), \(B:\)\(2\) occurs on either die \(C:\)The sum is at least \(7\), and a multiple of \(3\). Which pairs of these events are mutually exclusive?
Three coins are tossed once. Let \(A\) denote the event ‘three heads show”, \(B\) denote the event “two heads and one tail show”, \(C\) denote the event” three tails show and \(D\) denotes the event a head shows on the first coin”. Which events are (I) mutually exclusive? (ii) simple? (iii) Compound?