Question

A die is rolled, find the probability of following events:

1. A prime number will appear.

2. A number greater than or equal to 3 will appear.

3. A number less than or equal to one will appear.

4. A number more than 6 will appear.

5. A number less than 6 will appear.

Answer 1

Here sample space is S = {1, 2, 3, 4, 5, 6}

1. A: A prime number will appear A = {2, 3, 5};
P(A) = \(\frac{n(A)}{n(S)}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

2. B: A number greater than or equal to 3 will appear. B = {3, 4, 5, 6};
P(B) = \(\frac{n(B)}{n(s)} = \frac{4}{6} = \frac{2}{3}\)

3. C: A number less than or equal to one will appear. C = {1};
P(C) = \(\frac{n(C)}{n(S)} = \frac{1}{6}\)

4. D: A number more than 6 will appear.
D = Φ; P(D) = \(\frac{n(D)}{n(S)} = \frac{0}{6} = 0\)

5. E: A number less than 6 will appear. E = {1, 2, 3, 4, 5, 6};
P(E) = \(\frac{n(E)}{n(s)} = \frac{6}{6} = 1.\)