The amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.
The probability of an event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.
In the question, we are given that in a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. If she draws any other card, she loses.
We are asked the amount the woman should pay to play the game if it is fair.
The amount that the woman should pay to play the game is her expected return from the game.
Her expected return can be shown as E(X), where X represents all possible returns, which is calculated as:
E(X) = ∑ x.P(x), where P(x) is the probability of x.
The values of x can be:
3 when she draws a jack or a queen,
5 when she draws a king or an ace, and
0 when she draws any other card.
The probabilities of drawing a:-
The total number of possible outcomes remains constant throughout as 52.
Jack or a queen:
Number of favorable outcomes = 8 {4 jacks + 4 queens}.
Thus, the probability = 8/52 = 2/13.
King or an ace:
Number of favorable outcomes = 8 {4 kings + 4 ace}.
Thus, the probability = 8/52 = 2/13.
Any other card:
Number of favorable outcomes = 36 {All remaining cards, that is, 52 - 8 - 8 = 36}.
Thus, the probability = 36/52 = 9/13.
Thus, the expected return:
E(X) = ∑ x.P(x),
or, E(X) = 0.(9/13) + 3.(2/13) + 5(2/13),
or, E(X) = 0 + 6/13 + 10/13,
or, E(X) = 16/13 = 1.23.
Thus, the amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.
Learn more about the expected return and the probability of an event at
https://brainly.com/question/7965468
#SPJ2
