Kamila has two number cubes each labeled 1 to 6. She is going to conduct an experiment by tossing both cubes a total of 150 times. She will find the sum of the two numbers in each rolea. Possible outcomes? __________b. Probability of tossing a sum of six? _________c. How many times should Kamila toss a sum of 7? _________d. How many times should Kamila toss a sum of 10 or greater? _______
Accepted Solution
A:
a) There are 36 possible outcomes. b) The probability of a sum of 6 is 5/36. c) She should roll a sum of 7 45 times. d) She should roll a sum of 10 45 times.
Explanation a) There are 6 outcomes for the first die and 6 outcomes for the second one. By the fundamental counting principle, there are 6*6 = 36 outcomes for both dice together.
b) The ways to get a sum of 6 are: 1&5; 2&4; 3&3; 4&2; 5&1. There are 5 possibilities out of a total of 36, or 5/36.
c) The ways to get a sum of 7 are: 1&6; 2&5; 3&4; 4&3; 5&2; 6&1. There are 6 out of 36, or 6/36=1/6. Since she is rolling the dice 150 times, she should get a sum of 6 1/6(150) = 150/6 = 45 times.
d) The ways to get a sum of 10 or more are: 4&6; 5&5; 6&4; 5&6; 6&5; 6&6
There are 6 ways out of 36, or 6/36 = 1/6. Since she is rolling the dice 150 times, she should get a sum of 10 or more 1/6(150) = 150/6 = 45 times.