Register to reply

Probability with 2 dice

by Tasaio
Tags: dice, probability
Share this thread:
Tasaio
#1
Sep27-06, 06:08 PM
P: 20
Suppose we make 20 tosses using 2 dice. What is the probability of scoring a two numbers that sum to 7?

My attempt

The sample space for a single toss of a single die is S = {1, 2, 3, 4, 5, 6}

For a single toss of both dice, the sample space is
S = {(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 sample points with sum 7 are:
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)

These are 6 possibilties out of 36.

So for *each toss* of the 2 dice, there is a 6/36 probability of scoring two numbers that sum to 7.

My question is, how to we work out what the probabilty would be for 20 tosses?

If we have 20 tosses, then there are a total of 36*20 = 720 possible sample points. But how many of those possibilities contain numbers that sum to 7?
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
abode_x
#2
Sep27-06, 06:30 PM
P: 11
think of this one: 20 tosses of a single coin. what is the chance, you get a head?
the easiest approach is to count the chance no head appears (all tails for 20 tosses) and subtract it to 1.
Tasaio
#3
Sep27-06, 07:50 PM
P: 20
Quote Quote by Tasaio
Suppose we make 20 tosses using 2 dice. What is the probability of scoring a two numbers that sum to 7?

My attempt

The sample space for a single toss of a single die is S = {1, 2, 3, 4, 5, 6}

For a single toss of both dice, the sample space is
S = {(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 sample points with sum 7 are:
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)

These are 6 possibilties out of 36.

So for *each toss* of the 2 dice, there is a 6/36 probability of scoring two numbers that sum to 7.

My question is, how to we work out what the probabilty would be for 20 tosses?

If we have 20 tosses, then there are a total of 36*20 = 720 possible sample points. But how many of those possibilities contain numbers that sum to 7?
Using your coin example, on each toss, there is a 0.5 probability that there is a head.

So for 20 tosses, we calculate:
0.5 * 0.5 * 0.5 * ... * 0.5 (20 times)

Let's try that for my question.

For *each toss*, there is a 30/36 chance that the numbers do not sum to 7.

So after 20 tosses, the probability is:
(30/36) * (30/36) * (30/36) *...*(30/36) (with 20 terms)

= (5/6) * (5/6) *...* (5/6)
= ~0.026084

1 - 0.026084 = 0.973916

So there is a ~0.97 probablity that one of the tosses contains numbers that sum to 7.

This probability is very high. Does it sound about right?


Register to reply

Related Discussions
Dice Probability Precalculus Mathematics Homework 11
Need help with dice probability Set Theory, Logic, Probability, Statistics 12
Probability w/ dice Set Theory, Logic, Probability, Statistics 10
Probability of 5 dice rolled Precalculus Mathematics Homework 1
Probability with dice General Math 7