Subject
Quantitative Aptitude
Topic
Probability
In a city of 5 million people, there are 1 million politicians. 10 persons are selected randomly from the city. What is the probability that at most three of them are politicians?
In a city of 5 million people, there are 1 million politicians. 10 persons are selected randomly from the city. What is the probability that at most three of them are politicians?
ক)
1.688 × (4/5)7খ)
2.442 × (4/5)7গ)
2.096 × (4/5)7ঘ)
4.192 × (4/5)7ঙ)
6.288 × (4/5)7Explanation
In a city of 5 million people, there are 1 million politicians. ⇒ Probability that a randomly chosen person is politician = 1 million/5 million = 1/5 ⇒ Probability that a randomly chosen person is not a politician = 1 - 1/5 = 4/5 10 persons are selected randomly. To have at most three of them as politicians, there can be 0, 1, 2 or 3 politicians. Probability that there is 0 politician = 10 C 0 × (1 – (1/5)) 10 = 1 × (4/5) 10 = (4/5) 10 Probability that there is 1 politician = 10 C 1 × (1 – (1/5)) 9 × (1/5) 1 = 10 × (4/5) 9 × (1/5) = 2 × (4/5) 9 Probability that there are 2 politicians = 10 C 2 × (1 – (1/5)) 8 × (1/5) 2 = 45 × (4/5) 8 × (1/25) = (9/5) × (4/5) 8 Probability that there are 3 politicians = 10 C 3 × (1 – (1/5)) 7 × (1/5) 3 = 120 × (4/5) 7 × (1/125) = (24/25) × (4/5) 7 ∴ Probability that at most three of the chosen persons are politicians = (4/5) 10 + 2 × (4/5) 9 + (9/5) × (4/5) 8 + (24/25) × (4/5) 7 = 4.192 × (4/5) 7Related questions
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