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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b)
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.. +
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?
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).
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) =
A card is selected from the four cards shown, and this spinner is spun. c. Using this sample space, find the probability of getting: (1) an Ace and 1 on the spinner (2) a red card and 1 on the spinner (3) a picture card and 2 on the spinner (4) a black card and an odd number on the spinner (5) not an Ace and 3 on the spinner (6) a blue card and 2 on the spinner
. 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
a). A girl is randomly picking flowers in a meadow for a bouquet. She will stop once she has picked 4 dandelions. Suppose that a randomly selected flower is a dandelion with probability 0.70. Find the probability that her bouquet will have exactly 8 flowers in total. b). An entomologist has a collection of 20 insect specimens: 5 are butterflies and 15 are moths. He randomly selects a sample of 6 specimens to study. Find the probability that the sample contains an equal number of butterflies and moths. 2
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
Can someone help me out with these questions.
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?
Let A and B be two independent events of a sample space. If P(A)=pa and P(B)=pb, then the probability that at most one of them occurs is Select one: papb pa+pb−papb pa+pb−2papb None pa+pb 1−papb

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