The following table gives the life time of 400 neon lamps-Life time 0in hours - 300-400 400-500 500-600 600-700 700-800 800-900 900-1000 -Number of 14- 56 60 86 74 62 48 -lamps-A bulb is selected of random- Find the probability that the the life time of the selected bulb is-i less than 400ii between 300 to 800 hoursiii at least 700 hours-

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Standard IX

Mathematics

Coin Tossing Experiment

The following...

Question

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

Life time
(in hours) 300-400 400-500 500-600 600-700 700-800 800-900 900-1000

Number of lamps: 14 56 60 86 74 62 48

A bulb is selected of random, Find the probability that the the life time of the selected bulb is:
(i) less than 400
(ii) between 300 to 800 hours
(iii) at least 700 hours.

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Solution

The total number of trials is 400.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A₁ be the event that the lifetime of a chosen bulb is less than 400 hours.

The number of times A₁ happens is 14.

Therefore, we have

(ii) Let A₂ be the event that the lifetime of a chosen bulb is in between 300 to 800 hours.

The number of times A₂ happens is.

Therefore, we have

.

(iii) Let A₃ be the event that the lifetime of a chosen bulb is atleast 700 hours.

The number of times A₃ happens is.

Therefore, we have

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Similar questions

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

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

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.

Q. The following table gives the lifetimes of 400 neon lamps:

\begin{matrix} Lifetime & 300 - 400 & 400 - 500 & 500 - 600 & 600 - 700 & 700 - 800 & 800 - 900 & 900 - 1000 (in hr) Number & 14 & 56 & 60 & 86 & 74 & 62 & 48 of lamps \end{matrix}

(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a lifetime of more than 700 hours?

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Life time (months)	$9$	$10$	$11$	$12$	$13$	$14$	more than $14$
Number of Lamps	$26$	$71$	$82$	$102$	$89$	$77$	$53$

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

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

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Represent the given information with the help of histogram.

Life time (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 i)

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Q. The probability that a bulb selected at random has battery life greater than

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Life time (in hours)	300-400	400-500	500-600	600-700	700-800	800-900	900-1000
Number of lamps:	14	56	60	86	74	62	48