1. If A1, A2, and Az are three events and P(A, n Az ) = P(A, N A3 ) # 0 butP(A2 N Ay ) = 0, show thatP(at least one A,) = P(A, ) + P(A2 ) + P(A,) – 2P(A, n A2 )2. Suppose that two balanced dice are tossed repeatedly and the sum of theuppermost faces is determined on each toss. What is the probability that weobtaina) A sum of 3 betore we obtain a sum of 7?b) A sum of 4 betore we obtain a sum of 7?

As per the Bartleby guildlines we have to solve first question and rest can be reposted..... We have…

Answered: 1. If A, A2, and Az are three events…

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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Similar questions

If P(A)=0.7, P(B) = 0.75, P(C)= 0.8, P(AUB)=Q.8, P(AUC)=0.85, P(BUC)=0.9 and P(AUBUC)=0.95. find the probability of none of the three events occur اختر احدى الاجابات O 0.05 O 0.5 O None O 0.75 O 0.7
5. A candy dish contains 2 red (R) and 4 yellow (Y) candies. You close your eyes, select two candies from the dish (without replacement), and record their colors. Use general multiplication rule and special addition rule to find the following probabilities. a. The probability that the first selected candy will be red and the second selected candy will be yellow is b. The probability that two selected candies will be of different colors_ One is red, another one is yellow c. Probability that two selected candies will be of the same color_ Both are red or both are yellow Assuming that the event "The first selected candy will be red and the second selected candy will be yellow "is denoted by A, the event "Two selected candies will be of different colors" is denoted by B, and the event "Two selected candies will be of the same color" is denoted by C, show your work in finding P(A), P(B), and P(C) in the questions a, b, and c.
Suppose there are 6 red balls and 4 white balls in a urn.(1) event A={First draw is a white ball}, what is P(A), probability of A?(2) Now assume we do picking balls one by one without replacement. event B={Second draw is a white ball}, what is P(B), probability of B? (3) Are A and B independent? Justify your answer. please explain and do all the steps fully!
3
11.) A shipment of 11 printers contains 2 that are defective. Find the probability that a sample of 4, drawn from the 11, will not contain a defective printer.
Zia tossed a pair of fair dice 6 times. If the expected number of times that (a) a total of 7 or 11, (b) a matching pair, and (c) any other combination occurs are all greater than 2, she will ask help from her sister. Otherwise, she will ask help from his father. Who would she ask for help?
Hanna has a pair of 8-sided dice and if it rolls to 4,6 or 10 marie wins, if it rolls 9 or 13, marie loses For example, in case 7 comes out first, it is a tie so you need to roll it again and get 7 since it was your last number, if you get 7 again on your next few rolls, you win. but if you get 10, you lose what is the probability of marie winning the game? is she at disadvantage based on the rules? explain why or why not using computed probability of winning
There are three containers, A, B and C. Each container contains 25 balls, which are either red or blue. Container A has 15 red balls, container B has 16 red balls, and container C has 12 red balls. In a random experiment, one first randomly chooses a container, and then a ball is drawn from the chosen container. The probability of choosing container B in step 1 is 2/5 . The experiment is designed so that the events “the ball drawn is red” and “the ball drawn comes from container A” are independent. Suppose that the ball drawn is red. What is the probability that it came from container C?
6. Let A, B, C be three events with P(A) = P(B) = P(C) = 1, P(AC) = 1, P(AB) = P(BC) = 0, determine the probability of the event that at least one of A, B, C occurs.
Three groups of children contain respectively 3 girls and I boy: 2 girls and 2 boys: 1 girl and 3 boys. One child is selected at random from each group, Show that the chance that the three selected consist of 1 girl and 2 boys is 13/32?
7. A container has 5 red dice, 3 green dice and 4 black dice. If you randomly pick 2 marbles from the bag. one at a time, what is the probability that both will be red?
Show that the multiplication law P(AB) = P(A/B) P(B), established for two events, may be generalized to three events as foilows; P(AOBOC) = P(A/BOC) P(B/C) P(C)

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