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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) =1612536=1612536(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.

Syllabus sections

Topic 5 - Core: Statistics and probability » 5.2 » Concepts of trial, outcome, equally likely outcomes, sample space (U) and event.

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