c. Mysuru Mahanagar Palike surveyed the travel preferences of people who travelled to work
by train or bus. The initial analysis suggested that 1 in 5 people travelled by train to work. If
5 people are interviewed, what is the probability that,
1) Exactly 3 prefer travelling by train
2) Three or more prefer travelling by train and
3) Less than 3 prefer travelling by train.
Answers
Given : 1 in 5 people travelled by train to work.
5 people are interviewed,
To Find : probability
1) Exactly 3 prefer travelling by train
2) Three or more prefer travelling by train and
3) Less than 3 prefer travelling by train.
Solution:
1 in 5 people travelled by train to work.
=> p = 1/5 = 0.2
q = 1 - p = 1 - 0.2 = 0.8
n = 5
P(x) = ⁿCₓpˣqⁿ⁻ˣ
Exactly 3 prefer travelling by train
x = 3
=> P(3) =⁵C₃(0.2)³(0.8)² = 0.0512
Three or more prefer travelling by train
= P(3) + P(4) + P(5)
= ⁵C₃(0.2)³(0.8)² + ⁵C₄(0.2)⁴(0.8)¹ + ⁵C₅(0.2)⁵(0.8)⁰
= 0.0512 + 0.0064 + 0.00032
= 0.05792
Less than 3 prefer travelling by train.
= 1 - (P(3) + P(4) + P(5))
= 1 - 0.05792
= 0.94208
Or
P(0) + P(1) + P(2)
= 0.32768 + 0.4096 + 0.2048
= 0.94208
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