Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
June 2022 p51 q6
2652
Janice is playing a computer game. She has to complete level 1 and level 2 to finish the game. She is allowed at most two attempts at any level.
For level 1, the probability that Janice completes it at the first attempt is 0.6. If she fails at her first attempt, the probability that she completes it at the second attempt is 0.3.
If Janice completes level 1, she immediately moves on to level 2.
For level 2, the probability that Janice completes it at the first attempt is 0.4. If she fails at her first attempt, the probability that she completes it at the second attempt is 0.2.
(a) Show that the probability that Janice moves on to level 2 is 0.72.
(b) Find the probability that Janice finishes the game.
(c) Find the probability that Janice fails exactly one attempt, given that she finishes the game.
Solution
(a) The probability that Janice moves on to level 2 is calculated as follows:
She can complete level 1 on the first attempt with probability 0.6, or fail the first attempt and complete it on the second attempt with probability \(0.4 \times 0.3 = 0.12\).
Thus, the probability she moves on to level 2 is \(0.6 + 0.12 = 0.72\).
(b) The probability that Janice finishes the game is calculated by considering the successful paths:
Completes level 1 on the first attempt and level 2 on the first attempt: \(0.6 \times 0.4 = 0.24\)
Completes level 1 on the first attempt and level 2 on the second attempt: \(0.6 \times 0.6 \times 0.2 = 0.072\)
Completes level 1 on the second attempt and level 2 on the first attempt: \(0.4 \times 0.3 \times 0.4 = 0.048\)
Completes level 1 on the second attempt and level 2 on the second attempt: \(0.4 \times 0.3 \times 0.6 \times 0.2 = 0.0144\)
