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] = _nC_r p^rq^(n-r) , r = 0,1,2,...,n

P[X=r] = ₅C_r (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] = _nC_r p^rq^(n-r) , r = 0,1,2,...,n

P[X=r] = ₅C_r ( 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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