Question

The following table gives the life time of 400 neon lamps:

$\begin{array}{cccccccc}\text{Life time (in hours)}& 300-400& 400-500& 500-600& 600-700& 700-800& 800-900& 900-1000\\ \text{Number of lamps}& 14& 56& 60& 86& 74& 62& 48\end{array}$

A bulb is selected at random. Find the probability that the life time of the selected bulb is:

(i) less than 400 (ii) between 300 to 800 hours (iii) at least 700 hours.

Answer 1

Total number of neon lamps (n) =400

$\begin{array}{cccccccc}\text{Life time (in hours)}& 300-400& 400-500& 500-600& 600-700& 700-800& 800-900& 900-1000\\ \text{Number of lamps}& 14& 56& 60& 86& 74& 62& 48\end{array}$

(i) No. of bulbs having life time less than 400 hours(m) =14

$\therefore$ Probability P(A) =$\frac{m}{n}=\frac{14}{400}=\frac{7}{200}$

(ii) No. of bulbs having life time between 300 to 800 hours(m) =$14+56+60+86+74=290$

$\therefore$ Probability P(A) =$\frac{m}{n}=\frac{290}{400}=\frac{29}{40}$

(iii) No. of bulbs having life time at least 700 hours (m)=$74+62+48=184$

$\therefore$ Probability P(A) =$\frac{m}{n}=\frac{184}{400}=\frac{23}{50}$