Problem 36

Given information

     Given:-  You are playing a game by drawing a card from a standard deck of cards and replacing it. If the card is a face card, you win $. If it is not a face card, you                      pay $. There are face cards in a deck of cards.

  Concept:-  By multiplying values taken by random variable with respective probabilities, one obtains the expected value of the variable (random) or the Sum.

                  The total number of favorable outcomes of the particular event divided by total number of outcomes is called as the Probability of an event.

 To decide:- Whether the game should be played which results in a gain of $ (if a face card is picked up) and payout of $ if no face card is picked up out of a standard                    deck of cards.

Step-by-step explanation

As per the given question,

• Let be the amount gained while playing the game. If a face card is picked, you gain $ and if it is not face card then you lose $.
• So takes values and . This is because you will lose $, if you do not get a face card.  This amounts to a negative gain.
• Probability of getting a face card is , since the deck has face cards and one of cards out of a total of is picked up at random.
• There are (-) or cards which are not face cards. Hence, the probability of not getting face card .