Question

Lok Sabha in India is to discuss a key constitutional amendment, and there will be four
rounds of voting. In each round of voting, assume that the ruling party has a 60% chance
of winning, i.e. getting the resolution passed by majority vote. Further assuming that the
voting rounds are independent of each other, what is the probability that:
a. The ruling party will win 0 rounds, 1 round, 2 rounds, 3 rounds or all 4 rounds of
voting? (5 Marks)
b.The ruling party will win at least 1 round?

Answer 1

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:

$P(1, 2, 3, 4) = 1 - q^4 = 1- 0.0256 = 0.9744.$