A teacher proposes to his class to determine their grades by rolling two dice. The smaller number will be the grade. If the same number appears twice, this number will be the grade.
The easiest way to answer this riddle is to first enter all possible combinations in a table. Remember, the lower value "wins". In total, 36 variants are considered.
What is the probability to receive a 6?
This comparison shows that only once it is likely to receive a 6, particularly when the six is rolled twice. Its probability is 1 in 36.
What is the probability to receive a 1?
The grade 1 may be noted 11 times as its probability is 11 in 36 (or 30.56%).
What is the average grade?
To calculate the average grade, add all probabilities and divide by 36:
(11x1 + 9x2 + 7x3 +5x4 + 3x5 + 1x6) / 36 = 2.53
The average grade is 2.53.
Which grade is the most probable to receive?
Finally, it's most probable to receive a 1, as it is noted 11 times.