Further Mathematics Paper 2, May/June. 2010
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength

Question 15

(a) A manufacturer produces light bulbs which are tested in the following way: A batch is accepted in either of the following cases:
(i) The first sample of 5 bulbs contains no faulty bulbs;
(ii) The first sample of 5 bulbs contains at least one faulty bulb but a second sample of 5 bulbs contains no faulty bulb. If 10% of the bulbs are faulty, what is the probability that the batch is accepted?

(b) A bag contains 15 identical marbles of which 3 are back. Keshi picks a marble at random from the bag and replaces it. If this is repeated 10 times, what is the probability that he
(i) did not pick a black ball?
(ii) picked a black ball at most three times?

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Observation

The chief examiner reported that this was the least attempted question in Part II. The performance of the few who attempted it was reported to be generally poor. In rart (a), probability of having the first batch with no faulty bulbs was gotten by Co (0.1)°(0.9)5 == 0.59049. Probability of I" batch containing at least 1 faulty bulb and the second containing no faulty bulbs was given by (1 - 0.59049)(0.59049) =0.24181.

Therefore the probability of either the first condition or the second condition was 0.24181 + 0.59049 = 0.8323.
In part (b), probability of picking a black ball, p, == 3hs = lis, probability of not pickin~ a black ball, q, == 1 . lis = 415 and n = 10. Probability of picking no black ball == °Co (1/5)°(%)10 = 0.1074. Probability of picking a black ball atmost 3 times= IOClls)0(4/s) + lOCI els) 1(415)9 + IOC2(1/5)1 ~/s)8 + nC3 (1/5)3 (4/sf == 0.1074 + 0.2684 + 0.3020 + 0.2013 == 0.8791

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