A fair six-sided die is thrown twice and a fair coin is tossed thrice
MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability
Problem
A fair six-sided die is thrown twice and a fair coin is tossed thrice. All five trials are independent, and the order of occurrence is recorded.
Answer the following questions:
(i) Determine the total number of possible ordered outcomes.
(ii) Compute the probability that exactly one of the two throws of the die shows a 6 and exactly two of the three tosses of the coin show heads.
(iii) Compute the probability that the sum of the numbers obtained on the two dice is greater than 8 and at least two heads appear in the three coin tosses.
(iv) Compute the probability that at least one of the events described in parts (ii) or (iii) occurs.