You have a standard deck of 52 playing cards (13 of each suit). You draw a hand of the top 17 of them. Spades are one of the four suits. What is the expected value of the number of spades you draw?

Answer:The expected value of the number of spades are = 4.25Step-by-step explanation: As per the question,W know that in a standard deck of 52 playing card, there are 4 suits, and each suit have 13 playing card.Since, we know that [tex]Probability\ of\ a \ event\ = \frac{Number\ of\ Favorable\ Outcomes}{Total\ Number\ of\ Possible\ Outcomes}[/tex]Therefore,Probability of any random card being a spade is[tex]=\ \frac{13}{52}[/tex][tex]=\ \frac{1}{4}[/tex]So the expected number of spades we draw are[tex]=\ \frac{1}{4} \times 17[/tex][tex]=\ 4.25[/tex]Hence, the expected value of the number of spades are = 4.25