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I ASSIGNMENT EEE AND ICE (IV SEMESTER)

1. Urn A contains 9 white and 7 black balls. Urn B contains 12 black

and 10 white balls. A ball is randomly drawn from Urn A and placedin B and then a ball is transferred from Urn B to A. Finally, a ball is

selected from Urn A. hat is the probability that this ball is white!2. A man tosses a coin and throws a die be"innin" with a coin. hat is

the probability that he will "et a head before he "ets a #$% or #&% on

the die!'. A st(dent takes his e)amination in * s(b+ects ,-, ans /. e

estimates his chance of passin" in as *$, in - as , in as $&

and in / as 2'. 3o 4(alify he m(st pass in and atlest 2 other

s(b+ects. hat is the probability that he 4(alifies!*. A 2n di"it n(mber starts with the di"it 2 and all the di"its are prime.

3hen find the probability that the s(m of all two consec(ti5e di"its

of the n(mber is also prime!$. At an art e)hibition, there are 12 paintin"s of which 10 are ori"inal.

A 5isitor selects a paintin" at random and before he decides to b(y,

he asks the opinion of an e)pert abo(t the a(thenticity of the

paintin". 3he e)pert is ri"ht in 9 o(t of 10 cases on a5era"e.

6i5en that the e)pert decides that the paintin" is a(thentic, what isthe probability that this is really the case!f the e)pert decides that the paintin" is copy, then the 5isitor ret(rns

it and chooses another one8 what is the probability that his second

choice is ori"inal!&. n a certain colle"e * of boys and 1 of "irls are taller than

1&$cm. F(rther &0 of the st(dents are "irls. f a st(dent is selected

at random is taller that 1&$cm, what is the probability that the

st(dent is a "irl!7. f :A;

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9. et be a contin(o(s random 5ariable with p.d.f "i5en by

a) 0 ) 1

a 1 ) 2f:);

a) 'a 2 ) '

0 elsewhere

= + <

:i; Cetermine the constant a :ii; Cetermine F:);.10. A coin is tossed till a first head appears. et denote n(mber of

tosses and prob:;