Five cards are drawn successively with replacement from well- shuffled deck of 52 cards. What is the probability that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) None is a spade?
Five cards are drawn successively with replacement from well- shuffled deck of 52 cards. What is the probability that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) None is a spade?
Let X represent the number of spade cards among the five cards drawn. Since, the drawing card is with replacement, the trials are Bernoulli trails.
In a well-shuffled deck of 52 cards, there are 13 spade cards.
p=P(success) = P (a spade card is drawn) =1352=14 and q=1- 14=34.
X has a binomial distribution with n=5, p= 14 and q=34
Therefore, P(X=r)= nCrprqn−r,where r=0,1,2,..., n
P(X=r) =5Cr(14r)(34)5−r (By Binomial distribution)
(i) P (all the five cards are spades) = P(X=5)
= 5C5p5q0=1p5=145=111024=11024
Let X represent the number of spade cards among the five cards drawn. Since, the drawing card is with replacement, the trials are Bernoulli trails.
In a well-shuffled deck of 52 cards, there are 13 spade cards.
p=P(success) = P (a spade card is drawn) =1352=14 and q=1- 14=34.
X has a binomial distribution with n=5, p= 14 and q=34
Therefore, P(X=r)= nCrprqn−r,where r=0,1,2,..., n
P(X=r) =5Cr(14r)(34)5−r (By Binomial distribution)
P (only three cards are spades) = P(X=5)
=5C3p3q2 = 5.4.33!(14)3(34)2=601×2×3×3245=901024=45512
Let X represent the number of spade cards among the five cards drawn. Since, the drawing card is with replacement, the trials are Bernoulli trails.
In a well-shuffled deck of 52 cards, there are 13 spade cards.
p=P(success) = P (a spade card is drawn) =1352=14 and q=1- 14=34.
X has a binomial distribution with n=5, p= 14 and q=34
Therefore, P(X=r)= nCrprqn−r,where r=0,1,2,..., n
P(X=r) =5Cr(14r)(34)5−r (By Binomial distribution)
P (none is a spade)= P(X=0)= 5C0p0q5=1.q5(35)5=2431024
Let X represent the number of spade cards among the five cards drawn. Since, the drawing card is with replacement, the trials are Bernoulli trails.
In a well-shuffled deck of 52 cards, there are 13 spade cards.
p=P(success) = P (a spade card is drawn) =1352=14 and q=1- 14=34.
X has a binomial distribution with n=5, p= 14 and q=34
Therefore, P(X=r)= nCrprqn−r,where r=0,1,2,..., n
P(X=r) =5Cr(14r)(34)5−r (By Binomial distribution)
(i) P (all the five cards are spades) = P(X=5)
= 5C5p5q0=1p5=145=111024=11024
Let X represent the number of spade cards among the five cards drawn. Since, the drawing card is with replacement, the trials are Bernoulli trails.
In a well-shuffled deck of 52 cards, there are 13 spade cards.
p=P(success) = P (a spade card is drawn) =1352=14 and q=1- 14=34.
X has a binomial distribution with n=5, p= 14 and q=34
Therefore, P(X=r)= nCrprqn−r,where r=0,1,2,..., n
P(X=r) =5Cr(14r)(34)5−r (By Binomial distribution)
P (only three cards are spades) = P(X=5)
=5C3p3q2 = 5.4.33!(14)3(34)2=601×2×3×3245=901024=45512
Let X represent the number of spade cards among the five cards drawn. Since, the drawing card is with replacement, the trials are Bernoulli trails.
In a well-shuffled deck of 52 cards, there are 13 spade cards.
p=P(success) = P (a spade card is drawn) =1352=14 and q=1- 14=34.
X has a binomial distribution with n=5, p= 14 and q=34
Therefore, P(X=r)= nCrprqn−r,where r=0,1,2,..., n
P(X=r) =5Cr(14r)(34)5−r (By Binomial distribution)
P (none is a spade)= P(X=0)= 5C0p0q5=1.q5(35)5=2431024
