Question

Eric has two number cubes each labeled 1 to 6. Eric is going to conduct an experiment by tossing the cubes a total of 180 times. He will find the product of the two numbers in each roll.

a) How many possible outcomes are there? ____________
b) How many times should Eric toss a product of 12? ____________
c) How many times should Eric toss a product greater than 20? ___________
d) How many times should Eric toss a product less than 10? _________

Answer 1

The possible outcomes are:
$1,1~~1,2~~1,3~~1,4~~1,5~~1,6$
$2,1~~2,2~~2,3~~2,4~~2,5~~2,6$
$3,1~~3,2~~3,3~~3,4~~3,5~~3,6$
$4,1~~4,2~~4,3~~4,4~~4,5~~4,6$
$5,1~~5,2~~5,3~~5,4~~5,5~~5,6$
$6,1~~6,2~~6,3~~6,4~~6,5~~6,6$

The possible products are:
$1~~2~~3~~4~~5~~6$
$2~~4~~6~~8~~10~~12$
$3~~6~~9~~12~~15~~18$
$4~~8~~12~~16~~20~~24$
$5~~10~~15~~20~~25~~30$
$6~~12~~18~~24~~30~~36$


a) There are 36 outcomes.

b) 5/36 * 180 = 25

c) 6/36 * 180 = 30

d) 16/36 * 180 = 80