A student has the opportunity to take a test at most thrice.the student knows that each time he takes the test,his score is an independent random draw from the uniform distribution on the interval [0,100].
After learning his score on a test,the student can either stop and accept it as his official score,or he can discard the result and retake the test.If the student rejects his score twice and takes the test a third time,that score will be his official score.
If his objective is to maximise his expected official score,the student will decide to be retested after the very first test if and only if his score is less than....
Clear, the answer is a, because if his result is less than 50, then with probability more than 0:5 he will receive better results in the second or third trial. For instance, if he gets 75, then with only probability 0:15 he will get better result, so it is not reasonable to risk in this case.