Probability expected value exe
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 expectedamount she will make when she sells the cabinet?2. Three different people are selected at random and each given onegift card. The cards are from Panera Bread, Publix and OliveGarden. The first person chose chooses one card. The second persongets to choose one of the two remaining cards and the third persongets the third card. Determine the probability thata) The Panera Bread card is chosen firstb) The Publix card is chosen first and the Olive Garden card ischosen next and the Panera Bread card is chosen lastc) The Publix card is chosen second3. Ron has ten coins from Chile. four 1- peso coins, two 2- pesocoin, one 5-peso coins one 10-peso coin and two 20-peso coins. Heselects two coins at random without replacement. Assuming that eachcoin is equally likely to be selected, what is the probability heselects at least 1-peso one coin?4. If a card is drawn from a standard deck of cards, what is theprobability that the card is a red card, given that it is a facecard? Use the table below for the probability questions
Answer:
- 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. - We have three spaces as: _ _ _Sample SpaceThe three cards can be arranged in 3! = 6 waysCase IThe first card is fixed to be Panera Bread.The next two places can be filled in 2! = 2 ways.
Case IIThe first card is fixed to be Publix.The second card is fixed to be Olive Garden.The third card is fixed to bePanera BreadThere are no places left. This arrangement can be done in only oneway.
Case IIIThe 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.
- Ron has4 1-peso coins2 2-peso coins1 5-peso coin1 10-peso coin2 20-peso coinsHe chooses two coins without replacement.Let X be a random variable denoting the number of1-peso coins drawn.The pmf is given by:
We are to calculate
- In a deck of standard 52cards, there are 12 face cards.Face cards refer to those with a jack, king, orqueen on them. There are four suits in a deck ofcards and each suit has one of each type of theface 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.
The Expected profit is given as
Hence, the expected amount she will make when she sells it is$1965.
Case IIThe first card is fixed to be Publix.The second card is fixed to be Olive Garden.The third card is fixed to bePanera BreadThere are no places left. This arrangement can be done in only oneway.
Case IIIThe 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.
We are to calculate
I hope this clarifies your doubt. If you’re satisfied with thesolution, hit the Like button. For furtherclarification, comment below. Thank You. 🙂
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