Two students, Alice and Bob, occasionally miss their morning lectures. Let event AAA be the event that Alice misses the lecture and event BBB be the event that Bob misses the lecture. The probabilities are given as:
P(A)=0.40,P(A∩B)=0.12andP(A′∩B′)=0.55 P(A) = 0.40, \quad P(A \cap B) = 0.12 \quad \text{and} \quad P(A' \cap B') = 0.55 P(A)=0.40,P(A∩B)=0.12andP(A′∩B′)=0.55Find the probability that on a randomly chosen day:
At least one of Alice or Bob misses the lecture.
Bob misses the lecture.
Given that Alice missed the lecture, find the probability that Bob also missed it.
The professor believes that Bob missing the lecture might be related to Alice missing the lecture. Determine whether or not events AAA and BBB are statistically independent.
Comment on the professor's belief in light of your answer to part (d).
Practise Edexcel A Level Maths Conditional Probability with exam-style questions for A Level Maths. 152 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
