ProblemConsider a random experiment of throwing two fair dice together.Define the following events: A: { You roll a 6} & B: { At least one of the dice shows a 5 }(a) Identify the sample points in the events A, B, An B, AUB, and Aº.(b) Find P(A), P(B), P(A^ B), P(AUB), and P(AC).

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Answered: Problem Consider a random experiment of…

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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Part A number 4 please
Question 5 (a) Two independent events, A and B, are such that, P(A) = 0.7 and P(B) = 0.4, calculate: (i) P(AN B) (ii) P(A U B) (b) A team of 5 people is to be formed from 4 men and 6 women. Find the number of possible teams if there are: (i) No restrictions. (ii) More women than men on the team.
Consider the experiment of rolling two dice. Let A, B and C be 3 events defined by A = {First die results in a 1, 2 or 3} B = (Second die results in a 4, 5 or 6} C= {The sum of two faces is 7} Find: P(A U B) Choose.. + P(A n Bn C) Choose.. + P(A n B) Choose... + P(B | C) Choose.. +
Consider the following game: A player rolls two dice. If he rolls 7 or less then he loses the game. Otherwise, he selects at random as many cards from the full deck as the sum of the numbers that came up on the dice. The player wins if all four Aces are among the selected cards. (a) What is the winning probability for this game? (b) Someone tells that he played this game once and won. What is the probability that he rolled a sum of 10?
Consider two random events A and B. Event Ac is the complement of event A, and Bc is the complement of B. P(A) =0.64. P(B) = 0.3, and P(A and B) =0.192. Then we can say that the two events A and B are
(c) Given S be the sample space of an experiment of throwing an ordinary dice once, and A={5,6} ; B={4,5,6}, find the conditional probability of the conditional event A / B.
Naive Approach 1: Say A, B, C are independent ifP (A ∩B ∩C) = P (A)P (B)P (C).Suppose two six-sided dice are tossed and the outcome is noted. Let S denotethe sample space of this experiment.i. Write down the set S explicitly. Consider the eventsA = {(i, i) : i = 1, 2, 3, 4, 5, 6}, B = {(x, y) : 7 ≤x + y ≤10},C = {(x, y) : x + y is 2 or 7 or 8}.Write down the sets A, B, and C explicitly and calculate P (A), P (B), andP (C).
7. If an experiment the events A and B can both occur then a. P(A U B) = P(A)P(B|A) b. P(A N B) = P(A)P(A|B) c. P(AN B) = P(A)P(B|A) d. P(A U B) = P(B)P(B|A) %3D
In the diagram below, all circles represent products and the shaded circles represent defective products. If three items are drawn at random from the lot, what is the probability that they are not defective? оооо ооо оо оо 0000 0 а. 0.5113 0 b. 0.4233 О с. 0.7234 Od. 0.8095 0 e. 0.0030
Which of the following statements of random experiments and events is NOT true? The set A = {(H,H), (H,T), (T,H), (T,T)} is %3D an event in tossing a coin three times. The set D = {M, F} is an event in selecting a student from a class. The set B = {7 of hearts, 7 of spades, 7 of diamonds, 7 of clubs} is an event of drawing a card from a regular deck. The set C = {1, 3, 5} is an event in rolling a dice.
3. Oil exploration : Let D and E be two events in a sample space. It is given that P (D) = 0.4, P (E) = 0.5 and P (DUE) = 0.8. (a) Are the events D and E disjoint? Are the events D and E independent? Then to oil exploration. We imagine two oil fields. The event B = "oil discovery on field 1", while the complementary event B' = "no oil on field 1". Similarly, the event C = "oil discovery on field 2", while C' = "no oil on field 2". We are given that P (B n C) = 0.06, P (B' n C) = 0.12, P (B n C') = 0.11 and P (B' n C') = 0.71. (b) Find the probability of oil on field 1. Assume that oil has been found on field 2. What is now the probability of oil on field 1? Assume that it has been proven that field 2 does not contain oil. What is now the probability of oil on field 1? Are events B and C independent?

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Problem Consider a random experiment of throwing two fair dice together. Define the following events: A: { You roll a 6} & B: { At least one of the dice shows a 5 } (a) Identify the sample points in the events A, B, An B, AUB, and AC. (b) Find P(A), P(B), P(An B), P(AUB), and P(AC).