a. If p = 0.6, q = 1 - 0.6 = 0.4,
"Pn(k) = Cn(k)*p^k*q^{n-k},"
then the probability that the ruling party will win 0 rounds is:
"P4(0) = q^4 = 0.4^4 = 0.0256;"
the probability that the ruling party will win 1 round is:
"P4(1) = 4!\/(1!\\times3!)\\times0.6^1\\times0.4^3 = 0.1536;"
the probability that the ruling party will win 2 rounds is:
"P4(2) = 4!\/(2!\\times2!)\\times0.6^2\\times0.4^2 = 0.3456;"
the probability that the ruling party will win 3 rounds is:
"P4(3) = 4!\/(3!\\times1!)\\times0.6^3\\times0.4^1 = 0.3456;"
the probability that the ruling party will win all 4 rounds is:
"P4(4) = 0.6^4 = 0.1296."
b.The probability that the ruling party will win at least 1 round is:
"P(1, 2, 3, 4) = 1 - q^4 = 1- 0.0256 = 0.9744."
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