8.) A jar contains two balls colored green and purple. An experiment consists of repeatedlydrawing one ball from the jar with replacement (this means the ball is put back in the jar eachtime) until two greens have been drawn or a ball has been drawn 3 times, whichever comes first.(a) Assuming order matters, write the sample space S for this experiment in set notation.(b) Are the outcomes in S equally likely?(c) Write the following event G in set notation: exactly one green ball was drawn.(d) Find the probability of event G.(e) Describe event G' in words.(f) Write event G' in set notation.(g) Find the probability of event G'.(h) Write the following event F in set notation: the second ball drawn was purple.(i) Find P(FG).(j) Find P(GUF).(k) Find P(G'N F).(1) Write the following event E in set notation: 3 green balls were drawn.(m) Find P(E).4

a) The sample space S for this experiment, with order matters, can be represented in set notation as…

Answered: 8.) A jar contains two balls colored…

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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Suppose 4 orange and 3 red identical objects are in a jar. A blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. The following tree diagram depicts all the possible random outcomes, but the branch probabilities are missing. 40 3 R a b Orange → Red C d e Orange Red Orange Red Note: For all questions below, please enter your answers in fraction form. a) What is the value of the branch probability d=? b) What is the value of the branch probability b=? c) What is the value of the branch probability f=? 70
Consider the following experiment. A coin is tossed three times and the upper face (head or tail) is recorded for each toss. Use a tree diagram to find the simple events for the experiment. (Enter your answers as a comma-separated list. Enter each simple event in the format (O1, O2, O3) where Oi is the outcome of the ith toss. Use H for heads and T for tails.)
Find the conditional probability of the given event when two fair dice (one red and one green) are rolled. The red one is 1, given that the green one is 1. Step 1 Begin by considering the sample spaces and the probabilities of the outcomes. Recall that for the experiment of rolling two dice (the first one red and the second one green) and observing the face-up number on each die, the sample space S is the following 36-element set. 36 S = Recall also that since both dice are fair, the outcomes are equally likely; that is, the probability of any one outcome is the same as that of any other. Because probabilities are never negative and the sum of the probabilities of all outcomes in a sample space must be 1, the probability of any one of the 36 equally likely outcomes is 1 (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5,2), (5, 3), (5,…
Q1: In the experiment of tossing a coin 3 times and record whether it lands heads or tails on each toss. Draw a tree diagram to list the items of the sample space and define the elements of the following events: A. Observing similar faces B. Observing more than one tail Then find: 1. P(A), P(B) 2. P(A B) 3. P(A UB) 4. Are A and B mutually exclusive events? Why?
(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.
2. Let E and F be events in a sample space S. (a) The probability of E or F occurring is P(E U F) = (b) If the events E and F have no outcome in common (that is, the intersection of E and F is empty), then the events So in drawing a card from a deck, the event E, "getting a heart," and the are called event F, "getting a spade," are , (c) If E and F are mutually exclusive, then the probability of E or F is P(E U F) =
T5.11. Your teacher has invented a "fair" dice game to play. Here's how it works. Your teacher will roll one fair eight-sided die, and you will roll a fair six-sided die. Each player rolls once, and the winner is the person with the higher number. In case of a tie, neither player wins. The table shows the sample space of this chance process. Teacher Rolls You Roll 1 3 4 5 6 7 8 1 2 3 4 6 (a) Let A be the event "your teacher wins." Find P(A). (b) Let B be the event "you get a 3 on your first roll." Find P(A U B). (c) Are events A and B independent? Justify your answer.
. Let’s toss a biased coin twice and check the face of the coin. The probability for head and tail are a and b, respectively.(a) Determine the sample space.(b) Let Ti denote the event that the face is tail at i-th toss. Check if T2 and T4 are independent events
34 Probab 12. A bag contains two red. two yellow, and three blue balls. In an experiment, one ball is drawn from the bag and its color is noted, and then a second half is drawn and its color noted, (i) Draw a tree diagram for this experiment. (ii) How many outcomes are there in the sample space? Gii) What are the outcomes in the event, "two balls of the same color are selected"? tonr Otherwisa the
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