Question

The ages of 30 workers in a factory are as follows

$$\begin{array}{cccccc}Age& 24& 25& 26& 27& 28\\ Frequency& 5& 7& 8& 4& 6\end{array}$$

(i) Find the probability that a worker selected at random is older than 25
(ii) Find the probability that the age of a worker is an odd number.
(iii) Find the probability that the age of a worker is an even number.
(iv) What is the sum of answers two and three? Why?

Answer 1

(i) Number of workers who are older than 25 = 8 + 4 + 6 = 18
Probability that a worker selected at random is older than 25 = $\frac{18}{30}$ = 0.6.
(ii) Number of workers whose age is an odd number = 7 + 4 = 11
Probability that age of a worker is odd = $\frac{11}{30}$
(iii) Number of workers whose age is an even number = 5 + 8 + 6 = 19
Probability that age of a worker is odd = $\frac{19}{30}$
(iv) Sum of answers two and three = $\frac{11}{30}$ + $\frac{19}{30}$ = 1. The sum is equal to 1 because the events are complementary and the sum of probabilities of complementary events is 1.