(a)[1]
Show that the probability of Janice reaching level 2 is $0.72$.
(b)[3]
Calculate the probability that Janice completes the game.
(c)[4]
Find the probability that Janice makes exactly one failed attempt, given that she finishes the game.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
Janice is taking part in a computer game. She has to clear level 1 and then level 2 in order to finish the game. At each level, she is allowed no more than two attempts.
• For level 1, the chance that Janice clears it on her first attempt is $0.6$. If her first attempt is unsuccessful, the probability that she clears it on her second attempt is $0.3$.
• Once Janice clears level 1, she goes straight on to level 2.
• For level 2, the chance that Janice clears it on her first attempt is $0.4$. If her first attempt is unsuccessful, the probability that she clears it on her second attempt is $0.2$.