Question:
Answer:
3,9,13,19,27,30,31,35,45,47,47,51,54,57,59,63,67,70,70,73,75,81,82,84,84,86,89,93,96,99
The required frequency table is as shown below.
Range | Frequency | Relative Frequency |
80+ (Grade A) | 9 | 30.00% |
60-80 (Grade B) | 6 | 20.00% |
40-60 (Grade C) | 7 | 23.33% |
Below 40 (Grade F) | 8 | 26.67% |
Total | 30 | 100.00% |
From the above it is apparent that to get a Grade B or better, the student has to score more than 60 marks whose probability is 0.3 + 0.2 = 0.5 i.e. 50% probability of a random student to get a grade of B or better. This is apparent from the fact that 15 students out of 30 have scored more than 60 marks and thus would secure a B grade as per the marking criteria.
The concept of relative probability and subjective probability are often used in day to day lives.
Example 1: While investing money in the various assets, one can look at the historical performance and based on the probability of boom and bust may calculate his/her portfolio returns and thereby make optimum allocation of money to an efficient portfolio.
Example 2: While scheduling an outdoor tour, whether holds the key which can be predicted based on the probability of bad weather at a particular based on historical data.
Example 3: Based on the relative probability of guessing the right answers in a multiple choice exam (based on past performance), a candidate may decide whether guessing is an advisable strategy or not.
Example 4: An HR manager based on the probability model built by collecting data through surveys of sample of employees can take decision as to whether introduction of official transport would be beneficial to the company or not.
Example 5: In betting in day to day life, invariably the rewards are calculated by taking into consideration the probability of winning. Lower the probability of a win, higher should be the rewards. Thus based on given rewards, a decision can be taken by a rational gambler whether to gamble or accept a particular bet or not.