Question

If one die is rolled once, then find the probability of each of the following events:

1. Number on the upper face is prime
2. Number on the upper face is even.

Solution:

'S' is the sample space.

S = {1, 2, 3, 4, 5, 6} ∴ n(S) = `square`

(a) Event A: Prime number on the upper face

A = {2, 3, 5} ∴ n(A) = `square`

∴ P(A) = `("n"("A"))/("n"("S"))`

∴ P(A) = `3/square` = `square`

(b) Event B: Even number on the upper face

B = {2, 4, 6} ∴ n(B) = `square`

∴ P(B) = `("n"("B"))/("n"("S"))`

∴ P(B) = `square/square = 1/2`

Answer 1

'S' is the sample space.

S = {1, 2, 3, 4, 5, 6} ∴ n(S) = \[\boxed{6}\]

(a) Event A: Prime number on the upper face

A = {2, 3, 5} ∴ n(A) = \[\boxed{3}\]

∴ P(A) = `("n"("A"))/("n"("S"))`

∴ P(A) = \[\frac{3}{\boxed{6}}\] = \[\frac{\boxed{1}}{\boxed{2}}\]

(b) Event B: Even number on the upper face

B = {2, 4, 6} ∴ n(B) = \[\boxed{3}\]

∴ P(B) = `("n"("B"))/("n"("S"))`

∴ P(B) = \[\frac{\boxed{3}}{\boxed{6}}\] = `1/2`