A single die is rolled. Find the probability of rolling an odd number or a number less than 4?

Solution:

Given that a single die is rolled.

Sample space = {1, 2, 3, 4, 5, 6}

Let P(A) be the probability of getting an odd number, where A = {1, 3, 5}

Let P(B) be the probability of getting a number less than 4, where B = {1,2,3}

A ⋂ B ={1, 3}

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

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

P(A ⋂ B) = 2/6 = 1/3

Let P be the required probability of getting an odd number or a number less than 4

P = P( A ⋃ B ) = P(A) + P(B) - P(A ⋂ B)

P( A ⋃ B ) = 1/2 + 1/2 - 1/3

P( A ⋃ B ) = 1 - 1/3

P( A ⋃ B ) = 2/3

Therefore, the probability of rolling an odd number or a number less than 4 is 2/3.

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A single die is rolled. Find the probability of rolling an odd number or a number less than 4?

Summary:

When a single die is rolled, then the probability of rolling an odd number or a number less than 4 is 2/3.