A fair coin is tossed once and a fair six-sided die is thrown once
MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
A fair coin is tossed once and a fair six-sided die is thrown once. The result of the coin toss is recorded as Heads (H) or Tails (T), and the result of the die throw is recorded as the number of dots on the upper face.
(i) List the elements of the sample space for the combined experiment.
(ii) Let the event A be “getting a Head on the coin” and the event B be “getting an even number on the die.” Find P(A), P(B) and P(A∩B).
(iii) Using the values obtained in part (ii), examine whether A and B are independent events. Give a clear justification for your answer.
(iv) If the die is biased such that the probability of getting an even number becomes 32 while the probability of Heads on the coin remains 21, and all other outcomes adjust proportionally, would your conclusion in part (iii) necessarily remain the same? Give reasons.