Question

Probability expected value exercises questions:

1. The owner of an antique store estimates that there is a 50% chance she will make $3000 when she sells an antique cabinet, a 30% chance she will make $1550 when she sells the cabinet and a 20% chance she will break even when she sells it. What is the expected amount she will make when she sells the cabinet?
2. Three different people are selected at random and each given one gift card. The cards are from Panera Bread, Publix and Olive Garden. The first person chose chooses one card. The second person gets to choose one of the two remaining cards and the third person gets the third card. Determine the probability that
a) The Panera Bread card is chosen first
b) The Publix card is chosen first and the Olive Garden card is chosen next and the Panera Bread card is chosen last
c) The Publix card is chosen second
3. Ron has ten coins from Chile. four 1- peso coins, two 2- peso coin, one 5-peso coins one 10-peso coin and two 20-peso coins. He selects two coins at random without replacement. Assuming that each coin is equally likely to be selected, what is the probability he selects at least 1-peso one coin?
4. If a card is drawn from a standard deck of cards, what is the probability that the card is a red card, given that it is a face card? Use the table below for the probability questions

Answer 1

1. Let X be a random variable denoting the profit the owner makes. The profit random variable is given as:
   
   The Expected profit is given as
   
   
   
   Hence, the expected amount she will make when she sells it is $1965.
   
   
   
2. We have three spaces as: _ _ _
   Sample Space
   The three cards can be arranged in 3! = 6 ways
   
   Case I
   The first card is fixed to be Panera Bread.
   The next two places can be filled in 2! = 2 ways.
   
   
   
   Case II
   The first card is fixed to be Publix.
   The second card is fixed to be Olive Garden.
   The third card is fixed to bePanera Bread
   There are no places left. This arrangement can be done in only one way.
   
   
   
   Case III
   The second card is fixed to be Publix.
   The first place can be filled in 2 ways.
   The last place can be filled with the only remaining card.
   
   
   
   
   
3. Ron has
   4 1-peso coins
   2 2-peso coins
   1 5-peso coin
   1 10-peso coin
   2 20-peso coins
   
   
   He chooses two coins without replacement.
   Let X be a random variable denoting the number of 1-peso coins drawn.
   The pmf is given by:
   
   We are to calculate
   
   
   
   
   
   
   
   
   
4. In a deck of standard 52 cards, there are 12 face cards. Face cards refer to those with a jack, king, or queen on them. There are four suits in a deck of cards and each suit has one of each type of the face card.
   The four suits are Hearts (red), Spades (black), Clubs (black), Diamonds (red).
   Thus, each suit has 3 face cards.
   Therefore, there are 6 red cards amongst these 12 face cards.
   
   
   
   
   
   

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