We roll four 6-sided dice. What are the probabilities of each of the following outcomes? A. All four show “6" B. None of the four show "6" C. Two show "1" and two show "6" D. None of the four show either "1" or "6"

We roll four 6-sided dice. What are the probabilities of each of the following outcomes? A. All four show “6" B. None of the four show "6" C. Two show "1" and two show "6" D. None of the four show either "1" or "6"

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

**Problem Statement:**

We roll four 6-sided dice. What are the probabilities of each of the following outcomes?

A. All four show “6”

B. None of the four show “6”

C. Two show “1” and two show “6”

D. None of the four show either “1” or “6”

Expert Solution

Step 1

“Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get the remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”

From the given information, four dice are rolled.

Total number of outcomes in the sample space is n(S) = 6⁴ = 1296.

For a single die, the probability of getting any number (1, 2,…, 6) is,

P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = 1/6

From the known information, all four dice were thrown independently.

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