7. Suppose you play a game with your parter. Your partner pick one card, then yo

Question

7. Suppose you play a game with your parter. Your partner pick one card, then you pick. Suppose now your parter picked two cards and you picked one. You got an Ace. Assume you know your partner got a pair of QQ, for you, you have two options. You can pick one, or just give up. If you give up, no lose no win. If you try to pick one more card to compare with your partner, from the remaining 49 cards, if you pick an another Ace, you will win 100, if you pick other card, you will lose 2. Which option you should choose? (You need to compare the expectations for the two options to get the full points)

Explanation / Answer

Answer to the question)

total cards left = 49

Number o Ace present in 49 cards = 3

.

there are two options:

Option I : do not pick up next car, in this case there is neither loss nor profit

So expected value of this option is 0

Now for the second option if the expected value is negative, we would got for option I , else if the expected value of second option is positive we will go for second option

.

Let us evaluate the expected value of second option:

Suppose I chose to pick a card. there are two cases possible:

Case I: I get Ace

Formula of probability is as follows:

Probablity = favorable outcomes / total number of outcomes

We got favorable outcomes = 3 aces

and total number of outcomes = 49 cards available to be picked up

P(Ace) = 3 /49

Profit = 100

.

Case II = I do not get ace

P(No Ace) = (49 -3)/49 = 46 /49

Porfit = -2 [ it is a loss that is why shown with a negative sign]

.

formula of expected value = Summation of x*p

Here , x denotes the profit value , and p denotes its respective probability value

.On plugging the values of Profit and their respective probabilities we get:

E = (3/49) *100 + (46/49) * (-2)

E = 300/49 - 92 /49

E = 208 /49

E = 4.2449

Thus we get to know that the expected profit for option II is 4.2449

.

Inference: Thus we get to know that the expected value of option I is Zero , and expected value of option II is a profit of 4.2449. Thus since the option II is more prospective, I would chose to pick the card.

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