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 probability of drawing face - card

A standard deck has 52 cards and 12 face - cards. So the probability $P(F)$ of drawing a face - card is $P(F)=\frac{12}{52}=\frac{3}{13}$.

Step2: Calculate probability of drawing non - face card

The probability $P(NF)$ of drawing a non - face card is $P(NF)=1 - P(F)=1-\frac{3}{13}=\frac{10}{13}$.

Step3: Calculate expected value

The value of drawing a face - card $V(F) = 10$ and value of drawing a non - face card $V(NF)=- 2$. The expected value $E$ is $E = P(F)\times V(F)+P(NF)\times V(NF)$. Substitute the values: $E=\frac{3}{13}\times10+\frac{10}{13}\times(-2)=\frac{30 - 20}{13}=\frac{10}{13}\approx0.77$.

Answer:

0.77