Answer to Question #182140 in Statistics and Probability for Macinia Lopez

Question

In a deck of cards which consists of cards number 1 to 5 a card is drawn randomly. Each player wins 35 pesos if the number on the card is odd and losses 35 pesos if tge number on the card is even. What is the expected value of his winning?

Answer 1

The probability that the number is even is $p = \frac{2}{5}$ (since there are two even numbers in the deck: 2 and 4).It is also the probability that the player will lose 35 pesos.

Likewise, the probability that a player will lose 35 pesos is $q = \frac{3}{5}$ (since there are 3 odd numbers in the deck).

We have a distribution series:

$\begin{matrix} x&{ - 35}&{35}\\ p&{\frac{2}{5}}&{\frac{3}{5}} \end{matrix}$

Then the expected value of winning is $M(x) = \sum {{x_i}} {p_i} = \frac{{ - 35 \cdot 2 + 35 \cdot 3}}{5} = \frac{{35}}{5} = 7$

Answer: 7 pesos