Question

Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you place the card back in the deck, shuffle the deck, and draw another card. You repeat this process until you have drawn 12 cards in all. What is the probability of drawing at least 5 hearts?

For the experiment above, let XX denote the number of hearts that are drawn. For this random variable, find its expected value and standard deviation.

E(X)=E(X)=
σ=σ=

Answer 1

Let X be the number of hearts that are drawn

P( Heart) = 13/52 = 1/4 = 0.25 = p

n= 12

Let X ~ Binomila ( 12, 0.25)

P( drawing at least 5 hearts)

= P( X >=5)

= 1 - P( X <5)

= 1- 0.8423

= 0.1577

Expected Value , E(X) = np = 12 *0.25 = 3

Standard deviation = = 1.5