You have a deck of 10 cards colored on one side—7 red and 3 blue. You plan to blindly select three cards, shuffling the deck after each selection. With the help of a probability tree, produce the full probability distribution or the random variable “number of red cards selected” in this experiment, assuming
a. Selection is “with replacement.” (You will return each card to the deck before selecting the next one.)
b. Selection is “without replacement.” (You will hold onto each card selected.)
c. For your results in part a, compute the expected number of red cards selected, along with the variance and standard deviation for the random variable “number of red cards selected.”
d. For your results in part b, compute the expected number of red cards selected, along with the variance and standard deviation for the random variable “number of red cards selected.”