Stage 9 - Q1 - 3 marks
Use the independent-event tree to find \(P(\text{neither event})\).
Hint
Multiply along a path; add only the separate paths you need.
Stage 9 - Q2 - 3 marks
Use the independent-event tree to find \(P(\text{exactly one of A and B})\).
Hint
Multiply along a path; add only the separate paths you need.
Stage 9 - Q3 - 3 marks
Use the independent-event tree to find \(P(\text{at least one of A and B})\).
Hint
Multiply along a path; add only the separate paths you need.
Stage 9 - Q4 - 3 marks
Use the independent-event tree to find \(P(\text{both events or neither event})\).
Hint
Multiply along a path; add only the separate paths you need.
Stage 9 - Q5 - 3 marks
The tree shows two independent events. Which complete outcome or outcomes are most likely? Give the probability of each.
Hint
A large first branch does not alone determine the most likely complete outcome.
Stage 9 - Q6 - 3 marks
Use the independent-event tree to find \(P(\text{exactly one of A and B})\).
Hint
Multiply along a path; add only the separate paths you need.
Stage 9 - Q7 - 3 marks
Use the independent-event tree to find \(P(\text{at least one of A and B})\).
Hint
Multiply along a path; add only the separate paths you need.
Stage 9 - Q8 - 3 marks
Use the independent-event tree to find \(P(\text{both events or neither event})\).
Hint
Multiply along a path; add only the separate paths you need.
Stage 9 - Q9 - 3 marks
The tree shows two independent events. Which complete outcome or outcomes are most likely? Give the probability of each.
Hint
A large first branch does not alone determine the most likely complete outcome.
Stage 9 - Q10 - 5 marks
Two independent alarms each trigger with probability \(p\). The probability that at least one triggers is \(\frac{15}{16}\). Find \(p\).
Hint
Start with the complement: neither alarm triggers.