**Title:** Probability with Dice**Description:**In this exercise, we explore the probabilities associated with rolling two six-sided dice. We're interested in two specific events:- **Event A:** The outcome where the total sum of the dice equals 9.- **Event C:** The outcome where both dice show the same number.**Task:**Determine the probabilities of the following conditional events:- \( P(C|A') \): The probability that the dice show the same number, given they do not sum up to 9.- \( P(C'|A') \): The probability that the dice do not show the same number, given they do not sum up to 9.**Instructions:**Calculate the probabilities, and then simplify your answers:1. \( P(C|A') = \) [Enter your answer and simplify it.]2. \( P(C'|A') = \) [Enter your answer and simplify it.]**Additional Notes:*** \( A' \) represents the complement of event A, i.e., the dice do not add up to 9.* \( C' \) represents the complement of event C, i.e., the dice do not show the same number.This activity will help reinforce concepts of conditional probability and the use of complements in probability calculations.

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Answered: Two fair six-sided dice are rolled. Let…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A = event the die comes up even When one die is rolled, six outcomes are possible. These outcomes are those where the die shows B=event the die comes up 2 or more C= event the die comes up at most 3 D= event the die comes up 6 each value between 1 and 6. Are events A and B mutually exclusive? O A. Yes. These events do not share any common outcomes. O B. No. These events do not share any common outcomes. O C. No. At least the outcome where the die comes up 6 is common for these events. O D. Yes. At least the outcome where the die comes up 6 is common for these events.
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Suppose that in a year of 365 days, it rains on 62 days. There is lightning on 13 days. There is both lightning and rain on 12 days. Compare the chance that a rainy day has lightning to the chance that a day with lightning has rain. Show your work here P(lightning | rain) = P(rain | lightning)
= Lisa is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.25. If the flight is on time, the probability that her luggage will make the connecting flight is 0.9, but if the flight is delayed, the probability that the luggage will make it is only 0.65. Suppose you pick her up at the Denver airport and her luggage is not there. What is the probability that Lisa's first flight was delayed? P(delayed) = (Do not round until the final answer. Then round to three decimal places as needed.)
If A and B are complements, then which of the following is true about the probability of B based on the probability of A? 1) P(B)=P(A)+1 2) P(B)=1-P(A) 3) P(B)=1/P(A) 4) P(B)=P(A)-1
Probability scientist Atli decides to play in a lottery where there are many prizes on offer. The odds of winning each ticket in the lottery are 1/100 or 0.01. Atli decides to try his luck and buys 10 tickets.a) What is the probability that Atli will win exactly one of the tickets?b) What is the probability that Atli will win at least one of the tickets?
9. By rewriting the formula for the Multiplication Rule, you can write a formula for finding P(A and B) conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B| A) = P(A) the information below to find the probability that a flight arrives on time given that it departed on time. The probability that an airplane flight departs on time is 0.92. The probability that a flight arrives on time is 0.86. The probability that a flight departs and arrives on time is 0.83. The probability that a flight arrives on time given that it departed on time is (Round to the nearest thousandth as needed.) . Use
A letter is picked from the sentence "JAMES LOVES EXAMS" by first choosing a word at random and then picking a letter from the chosen word. Let, J stand for the event " the word James is picked" H stand for the event " the letter "E" is picked" Then J and H are not independent but mutually exclusive J and H are independent and mutually exclusive J and H are neither independent nor mutually exclusive J and H are independent but not mutually exclusive
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Two fair six-sided dice are rolled. Let A = the event that the dice add to 9, and let C = the event that the dice show the same number. Find P(CJA') and P(C'JA'). ..... P(CJA') = (Simplify your answer.) P(C'JA') =-| (Simplify your answer.)