Question

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine
(i) P (2)   (ii) P (1 or 3)    (iii) P (not 3)

Answer 1

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

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(i) Find P(2)

Number of faces showing 2 = 3

P(2) = 3 / 6 = 1 / 2

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(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

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(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

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Final Answers:

(i) P(2) = 1 / 2
(ii) P(1 or 3) = 1 / 2
(iii) P(not 3) = 5 / 6