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CLASS XII MATHEMATICS NCERT SOLUTIONS

Probability

Miscellaneous ExerciseQuestions

1. A and B are two events such that P (A) 0. Find P (B/A) if:

(i) A is a suset of B

(ii) A B !

". A cou#le has two children.

(i) Find the #roailit$ that oth children are %ales & it is 'nown that at least one of the

children is %ale.

(ii) Find the #roailit$ that oth children are fe%ales if it is 'nown that the elder child is a

fe%ale.. u##ose that *+ of %en and 0."*+ of wo%en have ,re$ hair. A ,re$ haired #erson is selected

at rando%. -hat is the #roailit$ of this #erson ein, %ale Assu%e that there are eual

nu%er of %ales and fe%ales.

. u##ose that 0+ of #eo#le are ri,ht2handed. -hat is the #roailit$ that at %ost of 3 of a

rando% sa%#le of 10 #eo#le are ri,ht2handed

*. An urn contains "* alls of which 10 alls ear a %ar' 456 and the re%ainin, 1* ear a %ar' 476.

A all is drawn at rando% fro% the urn8 its %ar' noted down and it is re#laced. &f 3 alls are

drawn in this wa$8 find the #roailit$ that:

(i)

all will ear 456 %ar'.

(ii) not %ore than " will ear 476 %ar'.

(iii) at least one all will ear 476 %ar'.

(iv) the nu%er of alls with 456 %ar' and 476 %ar' will e eual.

3. &n a hurdle race8 a #la$er has to cross 10 hurdles. 9he #roailit$ that he will clear each hurdle

is5

.6

-hat is the #roailit$ that he will 'noc' down fewer than " hurdles

. A die is thrown a,ain and a,ain until three sixes are otained. Find the #roailit$ of otainin,

the third six in the sixth throw of the die.

;. &f a lea# $ear is selected at rando%8 what is the chan,e that it will contain *" 9uesda$

. An ex#eri%ent succeeds twice as often as it fails. Find the #roailit$ that in the next six trails8

there will e at least successes.

10.

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1". u##ose we have four oxes A8 B8 = and > containin, coloured %arles as ,iven elow:

Box Marle colour

?ed -hite Blac'A

B=

>

1

3;

0

3

"1

3

"1

@ne of the oxes has een selected at rando% and a sin,le %arle is drawn fro% it. &f the

%arle is red8 what is the #roailit$ that it was drawn fro% ox A8 ox B ox =

1. Assu%e that the chances of a #atient havin, a heart attac' is 0+. &t is also assu%ed that a

%editation and $o,a course reduces the ris' of heart attac' $ 0+ and #rescri#tion of certain

dru, reduces its chances $ "*+. At a ti%e a #atient can choose an$ one of the two o#tions

with eual #roailities. &t is ,iven that after ,oin, throu,h one of the two o#tions the #atientselected at rando% suffers a heart attac'. Find the #roailit$ that the #atient followed a

course of %editation and $o,a.

1. &f each ele%ent of a second order deter%inant is either ero or one8 what is the #roailit$ that

the value of the deter%inant is #ositive (Assu%e that the individual entries of the

deter%inant are chosen inde#endentl$8 each value ein, assu%ed with #roailit$1

2).

1*. An electronic asse%l$ consists of two su2s$ste%s sa$ A and B. Fro% #revious testin,

#rocedures8 the followin, #roailities are assu%ed to e 'nown:

P (A fails) ! 0."P (B fails alone) ! 0.1*

P (A and B fail) ! 0.1*

Evaluate the followin, #roailities.

13. Ba, & contains ?ed and Blac' alls and B && contains ?ed and + Blac' alls. @ne all is

transferred fro% Ba, & to a, && and then a all is drawn fro% a, &&. 9he all so drawn is found

to e ?ed in colour. Find the #roailit$ that the transferred all is Blac'.

=hoose the correct answer in each of the followin,:

1.

&f A and B are two events such that P (A) 0 and P ( )B A ! 18 then:(A) A B (B) B A (=) B ! (>) A !

1;. &f P ( )A B P (A)8 then which of the followin, is correct:

(A) P ( )B A C P (B) (B) P (A B) C P (A) . P (B)

(=) P ( )B A P (B) (>) P ( )B A ! P (B)

1. &f A and B are an$ two events such that P (A) D P (B) P (A and B) ! P (A)8 then

(A) P ( )B A ! 1 (B) P ( )A B ! 1

(=) P ( )B A ! 0 (>) P ( )A B ! 0