Stage 9 - Q1 - 2 marks
A and B are independent. \(P(A)=\frac{4}{7}\), \(P(B)=\frac{1}{4}\). Find \(P(\text{both A and B})\).
Hint
Translate the requested outcome into one probability for each event.
Stage 9 - Q2 - 2 marks
A and B are independent. \(P(A)=\frac{1}{2}\), \(P(B)=\frac{3}{5}\). Find \(P(\text{A and not B})\).
Hint
Translate the requested outcome into one probability for each event.
Stage 9 - Q3 - 2 marks
A and B are independent. \(P(A)=\frac{2}{3}\), \(P(B)=\frac{2}{5}\). Find \(P(\text{neither A nor B})\).
Hint
Translate the requested outcome into one probability for each event.
Stage 9 - Q4 - 2 marks
A bag has 3 red out of 6 counters. Draw, replace, mix and draw independently again. Find \(P(\text{two reds})\).
Hint
Multiply the two red probabilities.
Stage 9 - Q5 - 3 marks
A and B are independent. \(P(A)=\frac{4}{5}\) and \(P(A\cap B)=\frac{16}{35}\). Find \(P(B)\).
Hint
Reverse \(P(\text{A and B})\)=\(P(A)\)\(P(B)\).
Stage 9 - Q6 - 2 marks
A and B are independent. \(P(A)=\frac{3}{7}\), \(P(B)=\frac{1}{7}\). Find \(P(\text{A and not B})\).
Hint
Translate the requested outcome into one probability for each event.
Stage 9 - Q7 - 2 marks
A and B are independent. \(P(A)=\frac{5}{7}\), \(P(B)=\frac{1}{3}\). Find \(P(\text{neither A nor B})\).
Hint
Translate the requested outcome into one probability for each event.
Stage 9 - Q8 - 3 marks
A and B are independent. \(P(A)=\frac{1}{6}\) and \(P(A\cap B)=\frac{1}{8}\). Find \(P(B)\).
Hint
Reverse \(P(\text{A and B})\)=\(P(A)\)\(P(B)\).
Stage 9 - Q9 - 2 marks
A bag has 3 red out of 10 counters. Draw, replace, mix and draw independently again. Find \(P(\text{two reds})\).
Hint
Multiply the two red probabilities.
Stage 9 - Q10 - 5 marks
Two independent sensors detect a signal. Sensor A succeeds with probability \(\frac{3}{4}\). The probability both succeed is \(\frac{3}{5}\). Find \(P(\text{B succeeds})\), then \(P(\text{A fails and B succeeds})\).
Hint
Use independence twice, first in reverse.