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Friday, December 30, 2016

some more problems from binomial distribution for cbse ncert class xii mathematics probability

some more problems from binomial distribution for cbse ncert class xii  mathematics probability


4.Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades (ii) only 3 cards are spades and (iii) none is a spade?

Let X be the number of spades among the five cards.
Assume X follows Binomial distribution with
n = 5
p = (13/52) = ( 1 / 4 ) [13 spades among the 52 cards ]
q =1 -p
q = (3 / 4)
P[X=r] = nCr prq(n-r) , r = 0,1,2,...,n
P[X=r] = 5Cr (1/4)r(3/4)(5-r) , r = 0,1,2,...,5

P[all the five cards are spades ] = P[X=5] =5C5(1/4)5(3/4)(5-5) =( 1 / 1024 )

P[only three cards are spades ] = P[X=3] =5C3(1/4)3(3/4)(5-3) =(90/1024)=(45/512)

P[none is a spade ] = P[X=0] =5C0(1/4)0(3/4)(5-0) =(243/1024)


9.On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?

Let X be the number of questions he answered correctly out of the 5 questions. just by guessing
Assume X follows Binomial distribution with
n =5
p = ( 1 / 3 ) [one out the three possible answers is correct and the candidate is guessing ]
q = 1 – p = ( 2 / 3 )
P[X=r] = nCr prq(n-r) , r = 0,1,2,...,n
P[X=r] = 5Cr ( 1 / 3 )r( 2 / 3 )(5 - r) r = 0, 1 ,..., 5
P[ candidate would get four or more correct answers just by guessing ] = P[X=4] + P[X=5]
= 5C4 ( 1 / 3 )4( 2 / 3 )(5 - 4) + 5C5 ( 1 / 3 )5( 2 / 3 )(5 - 5) = ( 11/243 )
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link to index of other miscellaneous problems on probability of cbse ncert 12th mathematics

index of more problems on baye's theorem for ncert cbse mathematics 


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