At a parking, there are 100 vehicles, 60 of which are cars, 30 are busses and the remainder trucks.
a) If three vehicles are chosen as sample taking one from each category, what is the total number of selections?
b) If two vehicles are chosen from each category, what is the total number of selections?
If every vehicle is equally likely to leave, find the probability of
c) a truck leaving first.
d) a bus leaving first
e) a car leaving second if either a truck or bus had left first. [1 mark]
If three vehicles left one after another without returning to the parking, what is the probability of:
f) all there were cars?
g) First vehicle was car and 2nd and 3rd vehicles are trucks.
Answers
Is Q a and b are same......
Given : At a parking, there are 100 vehicles, 60 of which are cars, 30 are busses and the remainder trucks.
To Find : a) If three vehicles are chosen as sample taking one from each category, what is the total number of selections?
b) If two vehicles are chosen from each category, what is the total number of selections?
c) a truck leaving first.
d) a bus leaving first
e) a car leaving second if either a truck or bus had left first
If three vehicles left one after another without returning to the parking, what is the probability of:
f) all there were cars?
Solution:
Total vehicles = 100
Cars = 60
Buses = 30
Trucks = 100 - 60 - 30 = 10
three vehicles are chosen as sample taking one from each category,
Number of Selections = ⁶⁰C₁x ³⁰C₁ x ¹⁰C₁ = 60 * 30 * 10 = 18000
two vehicles are chosen from each category,
Number of Selections = ⁶⁰C₂x ³⁰C₂ x ¹⁰C₂ = 60 * 30 * 10 = 3,46,47,750
a truck leaving first. = 10/100 = 1/10 = 0.1
a bus leaving first. = 30/100 =3/10 = 0.3
car leaving second = car leaving not 1st x car leaving 2nd
= (40/100) * (60/99) = 24/99
=8/33
= 0.2424
all there were cars = ⁶⁰C₃/ ¹⁰⁰C₃ = (60 * 59 * 58) / (100 * 99 * 98)
= 0.2116
Learn More:
In a Family of 3 children find probability of having at least one boy ...
https://brainly.in/question/7700718
Assume that adults have iq scores that are normally distributed with ...
https://brainly.in/question/11133397