Question

Consider the following frequency distribution which gives the weight of 38 students of a class:

Weights (in kg)	31-35	36-40	41-45	46-50	51-55	56-60	61-65	66-70	Total
No. students	9	5	14	3	1	2	2	2	38

(i) Find the probability that the weight of a student in the class lies between 36-45 kg.

(ii) Give 2 events in the context, one having probability 0 and the other having probability 1.

Answer 1

We have,

Total number of students = 38

(i) As, the number of students in the class whose weight lies between 36-45 kg = 5 + 14 = 19

So, the probability that the weight of a student in the class lies between 36-45 kg = $\frac{19}{38}=\frac{1}{2}$

(ii) As, the number of students in the class whose weight is less than 31 kg = 0

So, the probabilty that the weight of a student in the class is less than 31 kg = $\frac{0}{38}=0$


Also, the number of students in the class whose weight lies between 31-70 kg = 38

So, the probabilty that the weight of a student in the class lies between 31-70 kg = $\frac{38}{38}=1$

Hence, the two events, one having probabilty 0 is " A student whose weight is less than 31 kg" and the other having probability 1 is " A student whose weight lies between 31-70 kg".