Jede tossed a cube with faces numbered with 2,4,6,8,10,12 the results are recorded in the table what is the largest discrepancy between the experimental and the expected probability of this experiment

Answer 1

To find the largest discrepancy between the experimental and the expected probability of this experiment, we first need to calculate the expected probability of each outcome when rolling the cube.

Since the cube has faces numbered 2, 4, 6, 8, 10, and 12, each face has a 1/6 probability of being rolled when no. of faces = total no of faces in a cube=6. We can calculate the expected probability of each outcome by multiplying the probability of each face by the number of times it appears on the cube:

Expected probability of rolling a 2: (1/6) = 1/6
Expected probability of rolling a 4: (1/6) = 1/6
Expected probability of rolling a 6: (1/6) = 1/6
Expected probability of rolling an 8: (1/6) = 1/6
Expected probability of rolling a 10: (1/6) = 1/6
Expected probability of rolling a 12: (1/6) = 1/6

Next, we can calculate the experimental probability of each outcome by looking at the results recorded in the table:

Experimental probability of rolling a 2: 40/100 = 2/5
Experimental probability of rolling a 4: 20/100 = 1/5
Experimental probability of rolling a 6: 10/100 = 1/10
Experimental probability of rolling an 8: 10/100 = 1/10
Experimental probability of rolling a 10: 10/100 = 1/10
Experimental probability of rolling a 12: 10/100 = 1/10

Now, we can calculate the discrepancies between the experimental and expected probabilities for each outcome:

Discrepancy for 2: |(1/6) - (2/5)| = |1/6 - 2/5| = |5/30 - 12/30| = |-7/30| = 7/30
Discrepancy for 4: |(1/6) - (1/5)| = |1/6 - 1/5| = |5/30 - 6/30| = |-1/30| = 1/30
Discrepancy for 6: |(1/6) - (1/10)| = |1/6 - 1/10| = |5/30 - 3/30| = |2/30| = 1/15
Discrepancy for 8: |(1/6) - (1/10)| = |1/6 - 1/10| = |5/30 - 3/30| = |2/30| = 1/15
Discrepancy for 10: |(1/6) - (1/10)| = |1/6 - 1/10| = |5/30 - 3/30| = |2/30| = 1/15
Discrepancy for 12: |(1/6) - (1/10)| = |1/6 - 1/10| = |5/30 - 3/30| = |2/30| = 1/15

Therefore, the largest discrepancy between the experimental and expected probability of this experiment is 7/30.