Answered: We roll 2 dice 4 times and we want to…

We roll 2 dice 4 times and we want to know the number of times the sum of the dice was 7. Find the distribution of probabilities.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

We roll 2 dice 4 times and we want to know the number of times the sum of the dice was 7. Find the distribution
of probabilities.

Video Video

Expert Solution

Step 1: Overview

When rolling a die, there are 6 possibilities i.e., 1, 2, 3, 4, 5, and 6.

When rolling two dice, there are 6² = 36 total possibilities.

Now, the possible scenarios in rolling two dice when the sum of the dice can be 7, are:

(1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1).

Hence, total possible cases = 6

Now, the probability of getting a sum of 7 (p) = number of favourable cases / total cases = 6/36 = 1/6

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