Date | May 2010 | Marks available | 7 | Reference code | 10M.1.hl.TZ1.7 |
Level | HL only | Paper | 1 | Time zone | TZ1 |
Command term | Find | Question number | 7 | Adapted from | N/A |
Question
Two players, A and B, alternately throw a fair six-sided dice, with A starting, until one of them obtains a six. Find the probability that A obtains the first six.
Markscheme
P(six in first throw) =16=16 (A1)
P(six in third throw) =2536×16=2536×16 (M1)(A1)
P(six in fifth throw)=(2536)2×16=(2536)2×16
P(A obtains first six) =16+2536×16+(2536)2×16+…=16+2536×16+(2536)2×16+… (M1)
recognizing that the common ratio is 25362536 (A1)
P(A obtains first six) =161−2536=161−2536(by summing the infinite GP) M1
=611=611 A1
[7 marks]
Examiners report
This question proved difficult to the majority of the candidates although a few interesting approaches to this problem have been seen. Candidates who started the question by drawing a tree diagram were more successful, although a number of these failed to identify the geometric series.