So. I need help with probability.

Question

The table shows the outcomes of rolling two number cubes at the same time and finding the product of the two numbers. If Abby rolls two number cubes a hundred times, about how many times would she expect a product greater than 10?

Answer 1

Here are the possible outcomes (with outcomes greater than 10 in bold):

 

Cube 1                                  Cube 2

                      1       2       3       4       5       6

             ----------------------------------------------

  1:                 1       2       3       4       5       6

  2:                 2       4       6       8      10     12

  3:                 3       6       9      12     15     18

  4:                 4       8      12     16     20     24

  5:                 5      10     15     20     25     30

  6:                 6      12     18     24     30     36

 

The Theoretical Probability = (number of successful outcomes) / (number of possible outcomes)

       P = 17/36

 

The Theoretical Probability is the expected value (because it is the most likely).  However outcomes from 0 to 36 are possible, but less and less likely with numbers further and further from 17 (out of 36).

 

So, instead of rolling 36 times, Abby rolls a hundred times.  What is (17/36)*100 ?

     (17/36)*100 = 47.22222222

 

Abby would expect products greater than 10 about 47 out of the 100 rolls (other values from 0 to 100 are possible, but less and less likely as they differ from 47).