Discussion Problems of the Day (15-06-11)

[varsha]

Q: 1 A deck of 52 cards contains 4 aces.if the cards are distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all four aces will be received by the same player ?

Q 2 State whether true or false

A risk averse individual that has to decide between two different lotteries will always prefer a lottery with less risk.

[Ashima]

Hi,

Can you please give the answers to these questions?

Thanks!!!

[barkha]

Hi Ashima,

Giving answers won't help.On this website we promote independent learning and capability building in  solving problems. So if you are stuck somewhere or you could not understand something about the question, feel free to ask.In fact you can also tell us to what extent you could solve or how you approached the problem.

We would be glad to help!

Warm Regards,
Varsha

[Ashima]

Hi,

Can you please check if my approach is correct.

Ace can go to any of the four players. So, total number of ways will be equal to 4^4.
Favorable cases = 4 ( as all the four aces can go to either A,B,C or D)

Thanks:)

[barkha]

Ashima,

Start by finding out total no ways in which 52 cards can be distributed among 4 people, 13 cards each. This works out out to be  52C13*39C13*26C13*13C13. true that each ace can go to any of the four players but there are other cards which are to to be distributed as well so that each receives 13 cards each. And no of favorable cases whereby all four aces go to one person is given by 4 times 4C4*48C9*39C13*26C13*13C13.(As there are four aces and 48 non ace cards and all aces can be received by any of four players)

[Swati Kanodia]

Hi Varsha,

Should this not be done in the following manner:

a) Select 1 player out of 4 - 4C1
All aces go to him - 4C4
For the other 9 cards - 48C9
Total ways of giving him cards - 52C13
Thus, prob = (4C1* 4C4 * 48C9)/52C13
Please tell if i am wrong...

[barkha]

Swati,

figure out the sample space and favorable no of cases for this question, what u have done is incomplete description of both.

[duck]

Hi Varsha and Swati..
both of you have given the same answer..

[barkha]

You are right, Swati. Some misinterpretation from my side.
Thanks duck :)

[poonam]

answer to the second question - False
there are cases when the risk averse person chooses to gamble or go for the risky option.
for instance if the insurance is too high , or if he is provided with an appropriate risk premium.

however, i had a doubt.
since both the situations involve gambling(risk taking) and there is no question of sure income. simple logic says he should go for the lottery with the lower risk .

which of the two approach is right ... kindly reply .

[barkha]

A risk averse individual dislikes risk but not at any cost, she would take into account  expected value of each lottery in her  decision. It depends on the expected utility over lotteries  whether she would go in for a gamble or not.

Please don't interpret risk averse as somebody who prefers a sure income over any and every set of lotteries.
A risk averse individual does not accept a fair gamble.

I could not understand your argument regarding insurance.
But an insurance can make a risk averse individual certainly better off if the utility he gets by sure income after paying premium charges is greater than expected utility over lotteries.
And yes even for a risk averse individual it is worth taking a risk if adequately compensated in terms of high risk premium.

[poonam]

Dear Barkha
by insurance what i meant was this -
a risk averse person doesn't prefer even insurance if the premium is too high , such that his utility from expected wealth becomes less than expected utility.

so your argument means , the statement is false right ??

[barkha]

Yes!