Question

two cards are drawn simultaneously(or successively without replacement) from a well shuffled pack of 52 cards. find the mean, variance and standard deviation of the number of kings.

Answer 1

Solution :
X can take values 0,1,20,1,2
P(X=0)P(X=0) = Probability of getting no red card
=26/52×25/51=26/52×25/51
=26/51=26/51
P(X=1)P(X=1) = Probability of getting one red card
=26/52×26/51+26/52×26/51=26/52×26/51+26/52×26/51
=26/51=26/51
P(X=2)P(X=2) = Probability of getting both red card
=26/52×25/51=25/102=26/52×25/51=25/102
x=0=>P(x=x)=25102x=0=>P(x=x)=25/102
x=1=>P(x=x)=26/51x=1=>P(x=x)=26/51
x=2=>P(x=x)=25102x=2=>P(x=x)=25/102
E(x)=0×25/102E(x)=0×25/102+1×26/51+2×25/102+1×26/51+2×25/102
=2651+50102=52+50102=2651+50102=52+50102
=102102=102102=1=1
∑P1x21=0×25/102+1×26/51+4×25/102∑P1x12=0×25/102+1×26/51+4×25/102
=26/51+100/102=102+100/102=26/51+100/102=102+100/102
=202/102=202/102
Mean =∑P1wi=1=∑P1wi=1
Variance =∑Pix21−(∑Pixi)2=∑Pix12−(∑Pixi)2
=202/102=202/102−1−1
=100/102=50/51=100/102=50/51