Probability models for random events — A/L Combined Mathematics

How do I practise Probability models for random events?

1 question with a worked solution

Check before you answer: Addition Rule Verification: Applying P(A ∪ B) = P(A) + P(B) - P(A ∩ B) without omitting the intersection term for non-exclusive events.

1. Two events A and B are independent with P(A) = 0.40 and P(B) = 0.50. What is the probability that at least one of the two events occurs, P(A ∪ B)?
   1. A) 0.60
   2. B) 0.20
   3. C) 0.70
   4. D) 0.90
   Check my answer

   Correct answer: C) 0.70

   For independent events, P(A ∩ B) = P(A) · P(B) = 0.40 × 0.50 = 0.20. By the general addition rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.40 + 0.50 - 0.20 = 0.70.

   Show worked solution

   Step 1: Independence gives P(A ∩ B) = P(A) · P(B) = 0.40 × 0.50 = 0.20. Step 2: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.40 + 0.50 - 0.20 = 0.70. Answer: 0.70.
   Modelled on: the A/L Combined Mathematics examination pattern

Get this auto-marked

Next in the syllabus

Where does Probability models for random events fit in the syllabus?

Year 2 · Term 3