Answer:
Expected value of drawing a card in this game on the first turn = 6
Step-by-step explanation:
Given - Consider a game in which players draw playing cards one at a time from a standard 52-card deck. If a player draws a face card (a jack, a queen, or a king), the player is awarded 16 points. Any other card drawn earns the player 3 points.
To find - What is the expected value of drawing a card in this game on the first turn?
Formula used -
Expected value, E[x] = ∑ x p(x)
where p(x) is the probability
Proof -
Total cards in a standard deck = 52
Total face cards = 12 (a jack, a queen, or a king)
Other cards = 40
Now,
Probability of getting a face card = [tex]\frac{12}{52}[/tex]
Probability of getting a other card = [tex]\frac{40}{52}[/tex]
So,
Expected value, E[x] = ∑ x p(x)
= (16)([tex]\frac{12}{52}[/tex]) + (3)([tex]\frac{40}{52}[/tex])
= [tex]\frac{192}{52} + \frac{120}{52}[/tex]
= [tex]\frac{312}{52}[/tex]
= 6
∴ we get
Expected value of drawing a card in this game on the first turn = 6
So,
The correct option is - B. 6 points
