Problem 35

Given information

To find: The expected value of playing the game which consists of a gain of $ if face card is picked and a loss of $ if no face card is picked.            

Explanation :-

          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 the values taken by the random variables with respective probabilities, the sum of the expected value of the random variable is obtained. 

                      If the total number of favorable outcomes of that event is divided by total number of outcomes, we get the Probability of the event.

Step-by-step explanation

As per the given question,

• Let X be the amount gained by playing the game. If a face card is picked, the person gains $, but he loses $ if it is not a face card.
• So X takes values and as the person looses $ if he does not get a face card.  It is a negative gain.
• Probability of getting a face card is  , since the deck has face cards and one card at a time is picked up at random.