Q. 223.7( 3 Votes )
Two cards are drawn simultaneously (without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards.
Answer :
We know that in a deck of 52 cards there are 26 red cards and 26 black cards.
Let X be the random variable associated with this experiment of drawing of red cards simultaneously.
∴ X can take values 0 ,1 or 2.
P(X = 0) = Probability of getting 0 number of red card
This means both cards drawn are black.
∴ P(X=0) = 
Probability of getting 1 red card and the other non – red = P (X = 1)
P(X = 1) = 
P (X =2) = Probability of getting 2 red cards
P(X = 2) = 
Probability distribution table for the above random experiment is –
Mean = ∑pixi
Mean = 
+ 
+ 
Mean = 1
Variance = ∑pixi2 - Mean2
Variance = 
+ 
+ 
- 12
∴ variance = 0.49
Mean = 1 & Variance = 0.49.
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