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 Further Mathematics Paper 2, Nov/Dec. 2013
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength
Question 15

Question 15

A company has four telephone lines.  The probability that at a given instance, any of the lines is engaged is . Find the probability that

1. all the lines are engaged;
2. two of the four lines are engaged and the other two are free;
3. none of the lines is engaged;
4. at least one of the four lines is engaged.
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Observation

It was reported that this question was not as popular as questions 13 and 14.  It was also reported to be poorly answered by majority of those who attempted it.  Candidates’ were expected to recognize that the probability problem followed a binomial probability distribution nCrprqr with n = 4, p =   and q = .  Probability that all lines were engaged was 4C440 =  or 0.2963.  Probability that 2 lines were engaged was 4C2 =  or 0.2963. Probability that none of the lines was engaged was 4C004 =  or 0.1975.  Probability that at least one line was engaged  =  (1 – probability that no line was engaged) i.e. 1 – (4C0)= 1 -  =  or 0.8023.