In a cooperative society, 60 people go to the same office. They all use their own transport. 10 people use their scooters, 10 go by their cars and the rest use their motorcycles.
a) What is the probability of people going by motorcycles?
b) One day they all decided to go by cars but a car can accommodate only 5 people. What is the probability of people not going by cars now?
d) Which value is shown in 'b'.

Answer :

We know 

Probability P ( E ) = $\frac{Total number of desired events n (\hspace{0.17em}E\hspace{0.17em})}{Total number of events n (\hspace{0.17em}S\hspace{0.17em})}$

Given Total number of people , go to same office , so n (  S ) =  60
And
They all use their own transport. 10 people use their scooters, 10 go by their cars and the rest use their motorcycles.

a ) Total number of people use motorcycles  = 6 0 - 10 - 10  =  40 , So

n (  S ) =  40

Then

Probability of people going by motorcycle  = $\frac{40}{60} = \frac{\mathbf{2}}{\mathbf{3}}$                                                             ( Ans )

b ) One day they all decided to go by cars but a car can accommodate only 5 people. 
And total numbers of cars  =  10  , So
People can go by car on that day  =  10 $\times$ 5 =  50 
So,
Total number of people not going by car n ( E ) =  60 - 50 = 10

Then

Probability of people not going by car   = $\frac{10}{60} = \frac{\mathbf{1}}{\mathbf{6}}$                                                             ( Ans )

c ) By using Car - pool people trying to conserve the environment  .