Math, asked by gaganks4672, 1 month ago

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

Answered by amitnrw
2

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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