Question

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? 0.77 1.69 1.85 2.31

Explanation:

Step1: Calculate the probability of drawing a face card

A standard deck has 52 cards. There are 12 face cards (4 K, 4 Q, 4 J). So the probability \(P(\text{face card})=\frac{12}{52}=\frac{3}{13}\).

Step2: Calculate the probability of drawing a non - face card

The number of non - face cards is \(52 - 12=40\). So the probability \(P(\text{non - face card})=\frac{40}{52}=\frac{10}{13}\).

Step3: Calculate the expected value

The formula for expected value \(E(X)=\sum_{i}x_{i}P(x_{i})\). Here, \(x_1 = 10\) (points for face card) and \(x_2=- 2\) (points for non - face card).

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Answer:

0.77