Question

$80$ bulbs are selected at random from a lot and their lifetime in hours is recorded as under.

$\begin{array}{cccccc}\text{Lifetime (in hours)}& 300& 500& 700& 900& 1100\\ \text{Frequency}& 10& 12& 23& 25& 10\end{array}$

One bulb is selected at random from the lot. What is the probability that the selected bulb has a life more than $500$ hours?

a) $\frac{27}{40}$

b) $\frac{29}{40}$

c) $\frac{51}{6}$

d) $1$

Answer 1

The correct option is (b): $\frac{29}{40}$

$\begin{array}{cccccc}\text{Lifetime (in hours)}& 300& 500& 700& 900& 1100\\ \text{Frequency}& 10& 12& 23& 25& 10\end{array}$

Total number of bulbs in the lot $=80$
Number of bulbs with life time of more than $500$ hours $=(23+25+10)=58$

Let E be the event that the chosen bulb's lifetime is more than $500$ hours.

$\therefore$ Required probability $=P\left(E\right)=\frac{58}{80}=\frac{29}{40}$