Stage 9 - Q1 - 2 marks
\(P(A)=\frac{3}{14}\). Find \(P(\text{not }A)\).
Hint
The probabilities of an event and its complement sum to one.
Stage 9 - Q2 - 2 marks
A bag has 7 red, 7 blue and 9 green counters. Choose one uniformly. Find \(P(\text{red or blue})\).
Hint
The word or joins two mutually exclusive colours.
Stage 9 - Q3 - 2 marks
A result is gold, silver or bronze. \(P(G)=\frac{7}{20}\), \(P(S)=\frac{1}{4}\). Find \(P(B)\).
Hint
All three possible results together have probability one.
Stage 9 - Q4 - 3 marks
A bag has 24 red, blue or yellow counters. One is chosen uniformly. Require \(P(R)=\frac13\) and \(P(B)=\frac12\). Find all three colour counts.
Hint
The three colours cover the whole bag.
Stage 9 - Q5 - 3 marks
Exactly one of A, B and C occurs on each trial. Their probabilities have ratio \(1:3:6\). Find all three.
Hint
Use the sum of the ratio parts as the denominator.
Stage 9 - Q6 - 3 marks
Choose a whole number uniformly from 1 to 14. Events are even and at most 5. Can their probabilities simply be added? Find \(P(\text{either})\).
Hint
List the outcomes that satisfy both descriptions.
Stage 9 - Q7 - 2 marks
A result is gold, silver or bronze. \(P(G)=\frac{7}{17}\), \(P(S)=\frac{3}{17}\). Find \(P(B)\).
Hint
All three possible results together have probability one.
Stage 9 - Q8 - 3 marks
A bag has 12 red, blue or yellow counters. One is chosen uniformly. Require \(P(R)=\frac13\) and \(P(B)=\frac12\). Find all three colour counts.
Hint
The three colours cover the whole bag.
Stage 9 - Q9 - 3 marks
Exactly one of A, B and C occurs on each trial. Their probabilities have ratio \(1:3:5\). Find all three.
Hint
Use the sum of the ratio parts as the denominator.
Stage 9 - Q10 - 5 marks
A fair draw from a bag must give red with probability \(\frac{3}{8}\) and blue with probability \(\frac{5}{12}\). All other counters are green. Find the smallest possible bag and each colour count.
Hint
A whole counter count must result from each target probability.