Question

Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Answer 1

Hint: To find out the probability of a desired outcome we are provided with the formulae
P(A) =n(E)/n(S)
Where,
P(A) = Probability of an event
n(E) = Number of desired outcome
n(S) = Total number of outcomes


Complete step by step explanation:
Assume that I stood in front of the school gate for an hour. And recorded the following data of vehicles passing by
Two-wheelers = 8
Three-wheelers = 2
Four-wheelers = 6
1. Total number of vehicles
= No. of two-wheelers + No. of three-wheelers + No. of four-wheelers
=8 + 2 + 6
=16
i.e. n(S), which is the total number of outcomes = 16
2. Observed vehicle is a two wheeler = 8
i.e. n(E), which is the desired outcome = 8
3. P(A) is the probability that the vehicle observed is a two-wheeler
Using formulae P(A) = n(E)/n(S)
And putting the values of n(E) and n(S) from step 1 and step 2
P(A) = $\dfrac{8}{{16}}$
Dividing the numerator and denominator by 8
P(A) = $\dfrac{{\dfrac{8}{8}}}{{\dfrac{{16}}{8}}}$
Simplifying the expression we get
P(A) = $\dfrac{1}{2}$
P(A) Probability that the vehicle observed is a two-wheeler = $\dfrac{1}{2}$


Note: You should note that it is not important to use the above mentioned values of the frequency of vehicles crossing the school gates. You can use your own assumed values.