Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.
Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.
As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.
Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).
Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.
Ram's statistically minded friend Rocky feels that Ram should not use just one criterion to decide on a plan. "Decision making has to bring in all the criteria together. That is what makes a decision sound," Rocky said.
"How do I do that?" Ram asked. "Simple," said Rocky. "Give a weight to each criterion, multiply the value of each criterion by its weight, and add up the products for each option."
Rocky explained with an example: "For each option there are two criteria, the probability of not making it to the wedding and the travel time. The probability of not reaching on time is 1 minus the probability of reaching on time. Say you hate the thought of missing the wedding after all this effort, so give that criterion a weight of 80%. You also want to keep the travel time low, so give that a weight of 20%. For each option, add up (value of each criterion times its weight) and compare the totals across options. Pick the option with the lowest total."
"That simple?" Ram asked. "Well, it is, for a start," Rocky admitted.
For reference, the five itineraries under discussion (labelled A to E on the x-axis of each bar chart) are:
A: Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by bus; Jaipur to Ajmer by train
B: Delhi to Bharatpur by taxi; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train
C: Delhi to Bharatpur by train; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
D: Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
E: Delhi to Bharatpur by train; Bharatpur to Jodhpur by bus; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train
Q129. Of the diagrams given as options, which one best represents the contribution of each of the two criteria to the overall score, for each of the five itineraries A to E listed above, where the bottom portion of each bar shows the contribution of the probability of NOT reaching the destination on time, and the top portion shows the contribution of travel time?