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25.
Decisions are often „risky‟ in the sense that their outcomes are not known with certainty. Presented with a choice between a risky prospect that offers a 50 percent chance to win $200 (otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighted by their probability of occurrence.) Preference for a sure outcome over risky prospect of equal expected value is called risk averse; indeed, people tend to be risk averse when choosing between prospects with positive outcomes. The tendency towards risk aversion can be explained by the notion of diminishing sensitivity, first formalized by Daniel Bernoulli in 1738. Just as the impact of a candle is greater when it is brought into a dark room than into a room that is well lit so, suggested Bernoulli, the utility resulting from a small increase in wealth will be inversely proportional to the amount of wealth already in one‟s possession. It has since been assumed that people have a subjective utility function, and that preferences should be described using expected utility instead of expected value. According to expected utility, the worth of a gamble offering a 50 percent chance to win $200 (otherwise nothing) is 0.50 * u($200), where u is the person's concave utility function. (A function is concave or convex if a line joining two points on the curve lies entirely below or above the curves, respectively). It follows from a concave function that the subjective value attached to a gain of $100 is more than 50 percent of the value attached to a gain of $200, which entails preference for the sure $100 gain and, hence, risk aversion.
Consider now a choice between losses. When asked to choose between a prospect that offers a 50 percent chance to lose $200 (otherwise nothing) and the alternative of losing $100 for sure, most people prefer to take an even chance at losing $200 or nothing over a sure $100 loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: the impact of an initial $100 loss is greater than that of the next $100. This results in a convex function for losses and a preference for risky prospects over sure outcomes of equal expected value, called risk seeking. With the exception of prospects that involve very small probabilities, risk aversion is generally observed in choices involving gains, whereas risk seeking tends to hold in choices involving losses.
Based on above passage, analyse the decision situations faced by three persons: Babu, Babitha and Bablu.
[1] Suppose instant and further utility of each unit of gain is same for Babu. Babu has decided to play as many times as possible, before he dies. He expected to live for another 50 years. A game does not last more than ten seconds. Babu is confused which theory to trust for making decision and seeks help of a renowned decision making consultant: Roy Associates. What should be Roy Associates' advice to Babu?
A. Babu can decide on the basis of Expected Value hypothesis.
B. Babu should decide on the basis of Expected Utility hypothesis.
C. “Mr. Babu, I'm redundant”.
D. A and B
E. A, B and C[2] Babitha played a game wherein she had three options with following probalilities: 0.4, 0.5 and 0.8. The gains from three outcomes are likely to be $100, $80 and $50. An expert has pointed out that Babitha is a risk taking person. According to expected utility hypothesis, which option is Babitha most likely to favour?
A. First
B. Second
C. Third
D. Babitha would be indifferent to all three actions.
E. None of the above.[3] Continuing with previous question, suppose Babitha can only play one more game, which theory would help in arriving at better decision?
A. Expected Value.
B. Expected Utility.
C. Both theories will give same results.
D. None of the two.
E. Data is insufficient to answer the question.[4] Bablu had four options with probability of 0.1, 0.25, 0.5 and 1. The gains associated with each options are: $1000, $400, $200 and $100 respectively. Bablu chose the first option. As per expected value hypothesis:
A. Bablu is risk taking.
B. Expected value function is concave.
C. Expected value function is convex.
D. It does not matter which option should Babu choose.
E. None of above.asked in XAT
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26.
Five people joined different engineering colleges. Their first names were Sarah (Ms.), Swati (Ms.), Jackie, Mohan and Priya (Ms.). The surnames were Reddy, Gupta, Sanyal, Kumar and Chatterjee. Except for one college which was rated as 3 star, all other colleges were rated either 4 star or 5 star.
The “Techno Institute” had a higher rating than the college where Priya studied. The three-star college was not “Deccan College.” Mohan‟s last name was Gupta but he didn't study at “Barla College.” Sarah, whose last name wasn‟t Sanyal, joined “Techno Institute.” Ms. Kumar and Jackie both studied at four-star colleges. Ms. Reddy studied at the “Anipal Institute,” which wasn‟t a five-star college. The “Barla College” was a five-star college. Swati‟s last name wasn't Chatterjee. The “Chemical College” was rated with one star less than the college where Sanyal studied. Only one college was rated five star.[1] Which is the correct combination of first names and surnames?
A. Mohan Gupta, Sarah Kumar, Priya Chatterjee
B. Priya Chatterjee, Sarah Sanyal, Jackie Kumar
C. Jackie Sanyal, Swati Reddy, Mohan Gupta
D. Mohan Gupta, Jackie Sanyal, Sarah Reddy
E. Jackie Chatterjee, Priya Reddy, Swati Sanyal[2] Which option gives a possible student - institute combination?
A. Priya – Anipal, Swati – Deccan, Mohan – Chemical
B. Swati – Barla, Priya – Anipal, Jackie – Deccan
C. Joydeep – Chemical, Priya – Techno, Mohan – Barla
D. Priya – Anipal, Joydeep – Techno, Sarah – Barla
E. Swati – Deccan, Priya – Anipal, Sarah – Techno[3] Mohan Gupta may have joined:
A. Techno – Institute which had 5 star rating
B. Deccan College which had 5 star rating
C. Anipal Institute which had 4 star rating
D. Chemical College which had 4 star rating
E. Techno – Institute which had 4 star rating[4] In which college did Priya study?
A. Anipal Institute
B. Chemical Institute
C. Barla College
D. Deccan College
E. Techno- Institute[5] The person with surname Sanyal was:
A. Sarah studying in Chemical College
B. Swati studying in Barla College
C. Priya studying in Deccan College
D. Jackie studying in Deccan College
E. Sarah studying in Techno- Instituteasked in XAT
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27.
The regular mathematics faculty could not teach because of being sick. As a stop gap arrangement, different visiting faculty taught different topics on 4 different days in a week. The scheduled time for class was 7:00 am with maximum permissible delay of 20 minutes. The monsoon made the city bus schedules erratic and therefore the classes started on different times on different days.
Mr. Singh didn't teach on Thursday. Calculus was taught in the class that started at 7:20 am. Mr. Chatterjee took the class on Wednesday, but he didn't teach probability. The class on Monday started at 7:00 am, but Mr. Singh didn't teach it. Mr. Dutta didn't teach ratio and proportion. Mr. Banerjee, who didn't teach set theory, taught a class that started five minutes later than the class featuring the teacher who taught probability. The teacher in Friday's class taught set theory. Wednesday's class didn't start at 7:10 am. No two classes started at the same time.
[1] The class on Wednesday started at:
A. 7:05 am and topic was ratio and proportion.
B. 7:20 am and topic was calculus.
C. 7:00 am and topic was calculus.
D. 7:20 am and topic was calculus.
E. 7:05 am and topic was probability.[2] The option which gives the correct teacher- subject combination is:
A. Mr. Chatterjee – ratio and proportion
B. Mr. Banerjee – calculus
C. Mr. Chatterjee – set theory
D. Mr. Singh – calculus
E. Mr. Singh – set theory[3] Probability was taught by:
A. Mr. Dutta on Monday
B. Mr. Dutta on Thursday
C. Mr. Singh on Wednesday
D. Mr. Singh on Monday
E. None of these[4] The option which gives a possible correct class time – week day combination is:
A. Wednesday – 7:10 am, Thursday – 7:20 am, Friday – 7:05 am
B. Wednesday – 7:20 am, Thursday – 7:15 am, Friday – 7:20 am
C. Wednesday – 7:05 am, Thursday – 7:20 am, Friday – 7:10 am
D. Wednesday – 7:10 am, Thursday – 7:15 am, Friday – 7:05 am
E. Wednesday – 7:20 am, Thursday – 7:05 am, Friday – 7:10 amasked in XAT
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28.
Four married couples competed in a singing competition. Each couple had a unique team name. Points scored by the teams were 2, 4, 6 and 8. The “Sweet Couple” won 2 points. The “Bindas Singers” won two more points than Laxman's team. Mukesh's team won four points more than Linas's team, but Lina's team didn't score the least amount of points. “Just Singing” won 6 points. Waheda wasn't on the team called “New Singers”. Sanjeev's team won 4 points. Divya wasn't on the “Bindas Singers” team. Tapas and Sania were on the same team, but it wasn't the “Sweet Couple”.
[1] Laxman's teammate and team's name were:
A. Divya and Sweet Couple
B. Divya and Just Singing
C. Waheda and Bindas Singers
D. Lina and Just Singing
E. Waheda and Sweet couple[2] The teams arranged in the ascending order of points are:
A. Bindas Singers, Just Singing, New Singers, Sweet Couple
B. Sweet Couple, New Singers, Just Singing, Bindas Singers
C. New Singers, Sweet Couple, Bindas Singers, Just Singing
D. Sweet Couple, Bindas Singers, Just Singing, New Singers
E. Just Singing, Bindas Singers, Sweet Couple, New Singers[3] The Combination which has the couples rightly paired is:
A. Mukesh, Lina
B. Mukesh, Waheda
C. Sanjeev, Divya
D. Sanjeev, Lina
E. Sanjeev, Wahedaasked in XAT
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29.
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30.