3. 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 b. The ruling party will win at least 1 round
Answers
0.9744 is the probability that: The ruling party will win at least 1 round
Step-by-step explanation:
Probability that ruling party will win = 0.6
Probability that ruling part will not win = 1 - 0.6 = 0.4
Total rounds = 4
ruling party will win 0 rounds = ⁴C₀ (0.6)⁰(0.4)⁴ = 0.0256
ruling party will win 1 rounds = ⁴C₁ (0.6)¹(0.4)³ = 0.1536
ruling party will win 2 rounds = ⁴C₂ (0.6)²(0.4)² = 0.3456
ruling party will win 3 rounds = ⁴C₃ (0.6)³(0.4)¹ = 0.3456
ruling party will win 4 rounds = ⁴C₄ (0.6)⁴(0.4)⁰ = 0.1296
The ruling party will win at least 1 round = 1 - Ruling party will win 0 rounds
= 1 - 0.0256
= 0.9744
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