3 Marks Each

Question 13 Marks

The probability that the bomb dropped from a plane over a bridge will hit the bridge is $1 / 5$. Two bombs are enough to destroy the bridge. If $6$ bombs are dropped on the bridge find the probability that the bridge will be destroyed.

Answer

$0.3446$

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Question 23 Marks

Find the constant $K$ for the following discrete probability distribution. Hence obtain mean of this distribution :$P(x)=K .{ }^4 P_x, x=0,1,2,3,4$

Answer

Mean $\frac{196}{65}$

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Question 33 Marks

A number is selected from the natural number $1$ to $100 .$ Find the probability of the vent that the selected number is a multiple of $3$ or $5.$

Answer

$\frac{6}{100} ; 0.47$

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Question 43 Marks

$3$ bulbs are defective in a box of $10$ bulbs. $2$ bulbs are randomly selected from this box. These bulbs are fixed in two bulb holders installed in a room. Find the probability that the room will be lighted after starting the electric supply. OR Draw Venn diagram for the following events $;(1)$ Mutually exclusive events. $(2)$ Union of events. $(3)$ Intersection of events.

Answer

$\frac{14}{15}$

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Question 53 Marks

Fit a linear equation from the following data for variable $(y)$ of a time series $n=4, \Sigma y=270, \Sigma t y=734$.

Answer

$b=11.8$

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Question 63 Marks

Average rain and yield of a crop per acre in the year of an orid region is given :

Particulars	Rainfall $(cm)$	Yieid of crop $(kg)$
mean	$18$	$970$
Standard Deviation	$2$	$38$
Correlation coefficient $=0.6$

Obtain Regression line of yield on rain and estimate the yield of the crop if it rains $20\ cms$.

Answer

Crop is $992.8\ kg$ rain is $20\ cm$. or $25.06, x=16$

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Question 73 Marks

Ten students were ranked on the basis of their proficiency in sports and general knowledge. The rank correlation co-efficient obtained from the data was found to be $0.2.$ Later on it was noticed that the difference in the ranks of the two attrihutes for one of the student was taken as $3$ instcad of $2 .$ final the correct value of rank correlation coefficient.

Answer

$r=0.23$

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Question 83 Marks

Compute the cost of living index number by the method of total expenditure from the following data for the year $2019 :$

Items	$A$	$B$	$C$	$D$	$E$
Unit	Quintal	$20 \ kg$	$10$ litre	dozen	Meter
Quantity of $2018$	$50 \ kg$	$18 \ kg$	$12$ litre	$20$ pieces	$14$ meter
Price of $2018$	$1200$	$340$	$30$	$15$	$12$
Price of $2019$	$1700$	$380$	$40$	$24$	$16$

Answer

$132.5$

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