You are challenged to a lucky draw game. If you draw a face card (K, Q, J) from a standard deck of cards, you earn 10 points. If you draw any other card, you lose 2 points. What is the expected value of a draw?

There are 3 face cards for each of the 4 suits, leading to a total possible gain of 120, there are 40 other cards leading to a total possible loss of 80.
120 - 80 = 40.
40 / 52 (total number of cards) = about .77

Final Answer:
The expected value of a draw is positive 0.77 points.
Hope I helped :)

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MrRoyal MrRoyal · Answer 2 · 2022-05-11T05:05:32-04:00

The expected value of a draw in the lucky draw game is 0.77

How to determine the expected value?

In a standard deck of cards, we have:

Cards = 52

K, Q or J = 12

So, the probability of getting the face cards (K,Q, J) is:

p = 12/52

The earning when any of these cards is drawn is:

Earn = 10

So, the probability of not getting the face cards (K,Q, J) is:

q = 1 - 12/52

The earning when any of these cards are not drawn is:

Earn = -2

The expected value is calculated using:

E(x) = Sum(x P(x))

So, we have:

E(x) = 12/52 10 + (1 - 12/52) * -2

Evaluate

E(x) = 0.77

Hence, the expected value of a draw is 0.77