Question

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

Question:

The following table gives the life time of 400 neon lamps Life time300-400 400-500 500-600 600-700 700-800 800-900 900-1000 (in hours) Number of lamps 14 56 60 86 74 62 48 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:

(i) The probability that the life time of the selected bulb is less than 400 is $\frac{7}{200}$

(ii) The probability that the life time of the selected bulb is between 300 to 800 hours is $\frac{29}{40}$

(iii) The probability that the life time of the selected bulb is atleast 700 hours is $\frac{23}{50}$

Explanation:

Given that the life time of the neon lamps is 400 hours.

(i) Let $A_{1}$ denote the event of the life time of the selected bulb is less than 400 hours.

The number of times $A_{1}$ occurs is 14.

Thus, we have,

$P\left(A_{1}\right)=\frac{14}{400}$

           $=\frac{7}{200}$

Thus, the probability that the life time of the selected bulb is less than 400 is $\frac{7}{200}$

(ii) Let $A_{2}$ denote the event of the life time of the selected bulb is between 300 to 800 hours.

The number of times $A_{2}$ occurs is $14+56+60+86+74=290$

Thus, we have,

$P\left(A_{2}\right)=\frac{290}{400}$

           $=\frac{29}{40}$

Thus, the probability that the life time of the selected bulb is between 300 to 800 hours is $\frac{29}{40}$

(iii) Let $A_3$ denote the event of the life time of the selected bulb is atleast 700 hours.

The number of times $A_3$ occurs is $74+62+48=184$

Thus, we have,

$P\left(A_{3}\right)=\frac{184}{400}$

           $=\frac{23}{50}$

Thus, the probability that the life time of the selected bulb is atleast 700 hours is $\frac{23}{50}$

Learn more:

(1) The following table gives the life times of neon lamps:

Length (in hours) Number of lamps

300 − 400 14

400 − 500 56

500 − 600 60

600 − 700 86

700 − 800 74

800 − 900 62

900 − 1000 48

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a lifetime of more than 700 hours?

brainly.in/question/1418607

(2) In a bag, there are 100 bulbs . Out of which 30 bulbs are defective ones , a bulb is taken out of the bag at random . Find the probability of the selected bulb to be a good one

brainly.in/question/2534627

Answer 2

Answer:

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