(a) Expand (1 + 7 ) , (b) The first four terms of the binomial expansion...

  

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(a) Expand (1 + 7 ) , (b) The first four terms of the binomial expansion of 1+ ax + bx + cx. Find the values of the constants a, b and c. (c) Hence find the coefficient of x in the expansion of in ascending powers of x are ( + ) (1 + -*)*. (1) (4) (4) (Total 9 marks) Q7. Twins Alec and Eric are members of the same local cricket club and play for the club's under 18 team. The probability that Alec is selected to play in any particular game is 0.85. The probability that Eric is selected to play in any particular game is 0.60. The probability that both Alec and Eric are selected to play in any particular game is 0.55. (a) By using a table, or otherwise: (i) show that the probability that neither twin is selected for a particular game is 0.10; (ii) find the probability that at least one of the twins is selected for a particular game; (iii) find the probability that exactly one of the twins is selected for a particular game. (b) The probability that the twins' younger brother, Cedric, is selected for a particular game is: 0.30 given that both of the twins have been selected; 0.75 given that exactly one of the twins has been selected; 0.40 given that neither of the twins has been selected. Calculate the probability that, for a particular game: (i) all three brothers are selected; (ii) at least two of the three brothers are selected. (a) Expand (1 + 7 ) , (b) The first four terms of the binomial expansion of 1+ ax + bx + cx. Find the values of the constants a, b and c. (c) Hence find the coefficient of x in the expansion of in ascending powers of x are ( + ) (1 + -*)*. (1) (4) (4) (Total 9 marks) Q7. Twins Alec and Eric are members of the same local cricket club and play for the club's under 18 team. The probability that Alec is selected to play in any particular game is 0.85. The probability that Eric is selected to play in any particular game is 0.60. The probability that both Alec and Eric are selected to play in any particular game is 0.55. (a) By using a table, or otherwise: (i) show that the probability that neither twin is selected for a particular game is 0.10; (ii) find the probability that at least one of the twins is selected for a particular game; (iii) find the probability that exactly one of the twins is selected for a particular game. (b) The probability that the twins' younger brother, Cedric, is selected for a particular game is: 0.30 given that both of the twins have been selected; 0.75 given that exactly one of the twins has been selected; 0.40 given that neither of the twins has been selected. Calculate the probability that, for a particular game: (i) all three brothers are selected; (ii) at least two of the three brothers are selected.