These Ten-Year-Series (TYS) worked solutions with video explanations for 2022 A Level H2 Mathematics Paper 2 Question 8 are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2022 A Level H2 Math Paper 2 Question 9
A game is played using a counter on a board.
• The counter starts from a point S at the bottom of the board and moves upwards (see diagram).
• When leaving S the counter is equally likely to move up to the left to junction L or up to the right to junction R.
• At every junction after S, the counter moves up to the left with probability $p$ or up the right with probability $q$, where $p+q=1$.
• The counter eventually arrives at one of the endpoints A, B, C, D, E or F.
(a)
Show that the probability the counter arrives at B is $2{{p}^{3}}q+\frac{1}{2}{{p}^{4}}$.
[2]
(a) Show that the probability the counter arrives at B is $2{{p}^{3}}q+\frac{1}{2}{{p}^{4}}$.
[2]
John and Kath each play this game, and their counters both arrive at B.
(b)
Find, in terms of $p$, a simplified fraction for the probability that Jon’s and Kath’s counters followed exactly the same route.
[4]
(b) Find, in terms of $p$, a simplified fraction for the probability that Jon’s and Kath’s counters followed exactly the same route.
[4]
The probability that a counter arrives at B is the same as the probability that a counter arrives at C.
(c)
Find the value of $p$.
[4]
(c) Find the value of $p$.
[4]
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