All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Firstly, the probability that a voter supports the Alliance party is a constant.
Secondly, each voter’s decision to vote for Alliance Party is independent of another voter’s decision.
Lastly, voters can only decide to vote or not vote for Alliance Party.

(ii)
$\mathrm{P}(A = 3) \mathrm{P}(A = 4) = 0.373$

(iii)
(a)
Since n is large, $np = 16.5 > 5 ~\&~ nq = 13.5 > %$, we can approximate A with a normal distribution.

(b)
Since n is large, $np = 16.5 > 5$, we cannot approximate A with a poisson distribution.

(iv)
$\mathrm{P}(A = 15) = 0.06864$

${30 \choose 15} p^{15} (1-p)^{15} - 0.06864$

$[p(1-p)]^{15} = 4.42503 \times 10^{-10}$

$p(1-p) = 0.2379$

$p = 0.39 \text{~or~} 0.61$

Since $p \textless 0.5, \Rightarrow p = 0.39$