Bello chooses a number randomly from 1 to 10. What is the probability that it is either odd or prime?

Analyze the question: We pick a number from 1 to 10 and want P(odd or prime). Since "or" is used, we must count numbers that are odd, or prime, or both, without counting any number twice.

Concept: P(A or B) = P(A) + P(B) − P(A and B)

Solution:

• Sample space: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, so n(S) = 10
• Odd numbers: {1, 3, 5, 7, 9}, so 5 numbers
• Prime numbers: {2, 3, 5, 7}, so 4 numbers
• Both odd and prime: {3, 5, 7}, so 3 numbers

Numbers that are odd or prime: {1, 2, 3, 5, 7, 9}, which is 5 + 4 − 3 = 6 numbers.

P(odd or prime) = 6/10 = 3/5

Answer: The working gives 3/5, which is option D.

Tip: In "or" questions, list the actual numbers that qualify. Writing the combined set {1, 2, 3, 5, 7, 9} avoids double-counting 3, 5 and 7. Also remember that 1 is not prime, and 2 is the only even prime, so 2 is the one number that is prime but not odd.