Given:
The die has 6 faces in total, distributed as follows:
Number 1 → 2 faces
Number 2 → 3 faces
Number 3 → 1 face
Total possible outcomes = 6
(i) Find P(2)
Number of faces showing 2 = 3
P(2) = 3 / 6 = 1 / 2
(ii) Find P(1 or 3)
Number of faces showing 1 = 2
Number of faces showing 3 = 1
Total favourable outcomes = 2 + 1 = 3
P(1 or 3) = 3 / 6 = 1 / 2
(iii) Find P(not 3)
Number of outcomes that are not 3 =
Faces showing 1 or 2 = 2 + 3 = 5
P(not 3) = 5 / 6
Final Answers:
(i) P(2) = 1 / 2
(ii) P(1 or 3) = 1 / 2
(iii) P(not 3) = 5 / 6
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?