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Further Mathematics Paper 2, Nov/Dec. 2007  
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) The probability that Isaka will be alive in 10 years time is 1 and the
                                                                                         6
probability that Ashatu will live for the next 20 years is 1.  
                                                                                  3
Find the probability that
(i) Isaka will be alive in 10 years time and Ashatu will  die before the next 20 years.
(ii) At least one of them will be alive in 8 years time.

(b) Six fair coins of the same size are tossed once.  Find, correct to three decimal places, the probability that

  • a head is obtained;
  • at least four heads are obtained.
  • _____________________________________________________________________________________________________
    Observation

    The performance of candidates in this question was quite good.  The probability that Isaka will be alive while Ashatu will die before the next 20 years is given by
         1  x      {1 – 1  }   =   2     =    1
         6          {      3 }        18          9

    The probability that atleast one of them will be alive in 8 years time
        =   1   x   1   +   1   x   2   +  5   x   1     =   4
              6       3         6       3        6        3          9

    The probability of obtaining a head in a toss of six fair coins  is
          6C1 (½ )(½)5     =       
                                           32.
    Probability of atleast four heads  =  Prob. of 4 or 5 or 6 heads
       6C4(½)4 (½)2  + 6C5(½)5 (½) +  6C6(½)6 (½)0   =  15   +  6  x  1    =   11  
                                                                                       64      64    64        32

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