Question

8.4 100 electric bulbs are selected from a lot and their lifetimes are recorded in the form of a frequency
table, as shown below. Analyse the data and answer the following questions:
Lifetime (in hours)
500
600
700
800
900
1000
Frequency
12
20
34
14
12
8
(a) If one bulb is chosen at random, what is the probability that it has a lifetime of exactly 800 hours?
(b) If one bulb is chosen at random, what is the probability that it has a lifetime of more than 600
hours?
(c) If one bulb is chosen at random, what is the probability that it has a lifetime of at least 800 hours?​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|cc}\sf life \: time \: ( hrs)&\sf Frequency\: (f)\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}\\\sf 500&\sf 12\\\\\sf 600 &\sf 20\\\\\sf 700 &\sf 34\\\\\sf 800&\sf 14\\\\\sf 900&\sf 12\\ \\ \sf 1000&\sf 8\\\\\ \: \frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}\\\sf & \sf \sum f = 100& \end{array}}\end{gathered}\end{gathered}\end{gathered}$

We know that

$\tt \longrightarrow \: Probability \: of \: event \: to \: happen \: is \: given \: by$

$\boxed{ \red {\bf \: P(E) =\dfrac{Number \: of \: favourable \: outcomes}{ Number \: of \: outcomes}}}$

$\bf \:\large \red{AηsωeR : a}$

(a) If one bulb is chosen at random, what is the probability that it has a lifetime of exactly 800 hours?

☆ Total number of outcomes = 100

☆ Number of favourable outcomes = 14

We know that,

$\tt \: P(E) =\dfrac{Number \: of \: favourable \: outcomes}{ Number \: of \: outcomes}$

$\tt\implies \:P(E) = \: \dfrac{14}{100}$

$\tt\implies \: \boxed{ \purple {\bf \: P(E) = \: 0.14}}$

$\bf \:\large \red{AηsωeR : b}$

(b) If one bulb is chosen at random, what is the probability that it has a lifetime of more than 600

hours?

☆  Number of outcomes = 100

☆ Number of favourable outcomes = 34 + 14 + 12 + 8 = 68

We know that

$\tt \:  P(E) =\dfrac{Number \: of \: favourable \: outcomes}{ Number \: of \: outcomes}$

$\tt\implies \:P(E) = \: \dfrac{68}{100}$

$\tt\implies \: \boxed{ \blue {\bf \: P(E) = \: 0.68}}$

$\bf \:\large \red{AηsωeR : c}$

(c) If one bulb is chosen at random, what is the probability that it has a lifetime of at least 800 hours?

☆  Number of outcomes = 100

☆ Number of favourable outcomes = 14 + 12 + 8 = 34

We know that

$\tt \:  P(E) =\dfrac{Number \: of \: favourable \: outcomes}{ Number \: of \: outcomes}$

$\tt\implies \:P(E) = \: \dfrac{34}{100}$

$\tt\implies \: \boxed{ \pink {\bf \: P(E) = \: 0.34}}$