binomial distribution problem for ncert cbse 12th mathematics probability

binomial distribution problem for ncert cbse 12th mathematics probability

1.A die is thrown 6 times. If getting an odd number is a success, what is the probability of (i) 5 successes (ii) at least 5 successes (iii) at most 5 successes?

Let X be the number of successes out of 6 throws

Assume X follows binomial distribution with

n = 6,

p = (3/6) = ( 1 / 2 )

q = 1 -p

q = ( 1 / 2 )

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

P[X=r] = ₆C_r ( 1 / 2 )^r( 1 / 2 )^{(6 - r)}

P[X=r] = ₆C_r ( 1 / 2 )⁶

P[ 5 successes ] =P[X=5] = ₆C₅ ( 1 / 2 )⁶ = (3 /32)

P[ at least 5 successes ] =P[X=>5]= P[X=5] +P[X=6]= (7/64)

P[ at most 5 successes ] =P[X<=5] =1 - P[X=6]= 1 - ₆C₆ ( 1 / 2 )⁶ = (63 /64)

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2.A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of

two successes.

Let X be the number of doublets out of 4 tosses of a pair of dice.

Assume X follows binomial distribution with

n = 4,

p = (6 / 36) [6 doublets out of 36 possible outcomes in one toss of a pair of dice]

p = ( 1 / 6)

q= 1 -p

q = (5 /6)

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

P[X=r] = ₄C_r (1/6)^r(5/6)^{(4 - r)} , r = 0,1,2,3,4

P[two successes] = P[X = 2] =₄C₂ (1/6)²(5/6)^{(4 – 2)} = (25/216)

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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 

This problem and the answer is from binomial distribution in the chapter on probability for class xii of cbse ncert 12^th mathematics and is useful for the students preparing for the board examination 

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