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]
= nCr prq(n-r) , r =
0,1,2,...,n
P[X=r]
= 6Cr ( 1 / 2 )r(
1 / 2 )(6 - r)
P[X=r]
= 6Cr ( 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)
===============================
>
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]
= nCr prq(n-r) , r =
0,1,2,...,n
P[X=r]
= 4Cr (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
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 12th
mathematics and is useful for the students preparing for the board
examination
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