Further Mathematics Paper 2, May/June. 2014
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Main
Weakness/Remedies
Strength

Question 13

The probabilities that Kofi, Kwasi and Ama will pass a certain examination are and x respectively. If the probability that only one of them will pass the examination is,find the:

1. value of x;
2. probability that at least one of them will pass the examination
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Observation

The Chief Examiner reported that majority of the candidates who attempted this question performed well in it.The Chief Examiner also observed that some candidates interpreted “at least” wrongly.
Majority of the candidates were reportedly able to show that if the probability that Kofi passed the examination, p(Ko), was, that of Kwasi, P(Kw), =, that of Ama, P(A) =x and the probability that only one of them passed was  , then
( )   +  -

Simplifying this gave x =  . The probability that at least one of them passed the examination was obtained as 1 – probability that none of them passed =
1 – () = 1 -  =  or 0.987.