Q. 16

# Two cards are drawn without replacement from a well-shuffled deck of 52 cards. Let X be the number of face cards drawn. Find the mean and variance of X.

Given : Two cards are drawn without replacement from a well-shuffled deck of 52 cards.

To find : mean (𝓊) and variance (σ2) of X

Formula used : Mean = E(X) = Variance = E(X2) - Mean = E(X) = = x1P(x1) + x2P(x2) + x3P(x3)

Two cards are drawn without replacement from a well-shuffled deck of 52 cards.

Let X denote the number of face cards drawn

There are 12 face cards present in 52 cards

P(0) = = = P(1) = = = P(2) = = = The probability distribution table is as follows, Mean = E(X) = 0( ) + 1( ) + 2( ) = 0 + + = = = Mean = E(X) =  = = E(X2) = = P(x1) + P(x2) + P(x3)

E(X2) = ( ) + ( ) + ( ) = 0 + + = E(X2) = Variance = E(X2) - =  = = Variance = E(X2) - = Mean = E(X) = Variance = Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Probability of occurrence of an event | Quiz Time45 mins  Probability of occurrence of an event45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 