Question

A pair of fair dice is rolled. What is the probability of each of the following? (Round your answers to three decimal places.) (a) the sum of the numbers shown uppermost is less than 7

Answer 1

36 ways for the dice to total 2 through 7
{1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1} // Total -> 36
15 ways for the doce to totol less than 7
{1, 2, 3, 4, 5} // Total -> 15

15/36 is the probability that the dice will show a total of less than 7.
15/36 = 0.417 rounded to the nearest 1/1000

Answer 2

total number of points in event space is 6^2=36. Now the sum is less than 7 when the sum is 2,3,4,5,6 Which is 1+1,1+2,2+1,1+3,3+1,1+4,4+1,1+5,5+1,2+3,3+2,2+4,4+2,2+2,3+3 that is in total 15 cases. required probability is 15/36=0.417 correct upto 3 decimal places/

Answer 3

@robtobey how did you come to the conclusion that the number of cases is 15, by hand calculation or with the help of any formula? Let me know///

Answer 4

Sent you a message. Not able to deal with this system any longer.

Answer 5

@Princer_Jones
The construct {2, 3, ... } is a Mathematica "list". Total is a Mathematica function that will sum the list elements. The calculations were done by Mathematica and the text input and output under Mathematica was copied and pasted into this browser's window. As an aside, now limited to the Google Chrome browser.

Some time ago I wondered how the odds for the casino game of craps came about. During that process it was determined that there was 1 way for 2 to show, 2 ways for a 3, 3 ways for a 4 and so forth.

There are 1+2+3+4+5 = 15 ways for a total of the two dice to come up 2, 3, 4, 5 and 6.
On the upper side of 7 there are 6 ways for an 8, 5 ways for a 7, 4 ways for a 6 and so forth until we encounter "box cars", 2 sixes. Only one way that can happen.

You can confirm the statements above by playing with two physical dice.

Answer 6

@robtobey thanks. i used to do hand calculations. :). thanks