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Probability
(a) Suppose you roll 3 dice consecutively. What is the probability that the values shown by the dice are in strictly increasing order?

(a) Suppose you roll 3 dice consecutively. What is the probability that the values shown by the dice are in strictly increasing order?

A First Course in Probability (10th Edition)
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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The first three sections asked about theoretical aspects of probability theory, but probability is also useful for doing computations! Try your hand at a few of the following problems! (a) Suppose you roll 3 dice consecutively. What is the probability that the values shown by the dice are in strictly increasing order? (b) Suppose there is a 50 percent chance that it rains on any given day. Moreover, assume that whether or not it rains on any given day is independent of whether or not it will rain on any other given day. What is the probability that it rains at least once in a 7 day week. (c) Suppose there are 25 people in a room, and each person has their birthday drawn uniformly at random from the 365 days of a year (sorry leap years!). What is the expected number of people that share a birthday with at least one other person?
Transcribed Image Text:The first three sections asked about theoretical aspects of probability theory, but probability is also useful for doing computations! Try your hand at a few of the following problems! (a) Suppose you roll 3 dice consecutively. What is the probability that the values shown by the dice are in strictly increasing order? (b) Suppose there is a 50 percent chance that it rains on any given day. Moreover, assume that whether or not it rains on any given day is independent of whether or not it will rain on any other given day. What is the probability that it rains at least once in a 7 day week. (c) Suppose there are 25 people in a room, and each person has their birthday drawn uniformly at random from the 365 days of a year (sorry leap years!). What is the expected number of people that share a birthday with at least one other person?
Expert Solution
Step 1: Given

A dice is thrown 3 times 

Therefore total number of outcomes in sample space is (6)3=216


Note : Since you have posted multiple questions therefore as per guidelines I have answered only the first question If you want the solution of the other 2 questions then post it again and mention it. 

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