There is a group of 100 people who are patriotic out of which 70 believe in non-violence. Two persons are selected at random out of them. Write the probability distribution for the selected persons who are non-violent. Also find mean of this probability distribution.
Answers
P(0) = 0.09 , P(1) = 0.42 , P(2) = 0.49 Mean = 1.4
Step-by-step explanation:
There is a group of 100 people
70 believe in non-violence
Probability of non Violence p = 70/100 = 0.7
q = 1 - p = 1 - 0.7 = 0.3
Probability Distribution = P(x) = ⁿCₓpˣqⁿ⁻ˣ
P(0) = ²C₀(0.7)⁰(0.3)² = 0.09
P(1) = ²C₁(0.7)¹(0.3)¹ = 0.42
P(2) = ²C₂(0.7)²(0.3)⁰ = 0.49
Mean = 0 * 0.09 + 1 * 0.42 + 2 * 0.49
= 0.42 + 0.98
= 1.4
or Mean = np = 2(0.7) = 1.4
Another Method : ( as after selecting one people probbaility for other changes)
P(0) = ³⁰C₂/¹⁰⁰C₂ = 0. 088
P(1) = ³⁰C₁*⁷⁰C₁/¹⁰⁰C₂ = 0.424
P(2) = ⁷⁰C₂/¹⁰⁰C₂ = 0. 488
Mean = 1.336
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