Question

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then, P(A ∪ B) is ______.

Options

• 2/5

• 3/5

• 0

• 1

Answer 1

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then, P(A ∪ B) is 1.

Explanation:

Given, A be the event that the number obtained is greater than 3.

∴ A = {4, 5, 6}

and B be the event that the number obtained is less than 5.

∴ B = {1, 2, 3, 4}

So, A ∩ B = {4}

By addition theorem of probability, we have

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

`\implies` P(A ∪ B) = (3 / 6) + (4 / 6) – (1 / 6) = 1