Experiment #1: Flipping a Coin. Assume heads and tails are equally likely to occur.1. What is the sample space for this experiment? How many possible outcomes?2. For each of the following, compute p(E), the probability of event E occurring when a coinis flipped 3 times.(a) p(0 heads)(b) p(1 heads)(c) p(at least 1 heads)(d) p(at least 2 heads)3. Consider the experiment where a coin is flipped 10 times in a row. Answer the following.(a) How many possible outcomes are there in this experiment?(b) How many outcomes contain exactly 0 heads? 1 heads? 2 heads? 3 heads? k heads?(c) p(7 heads)(d) p(at least one heads)(e) p(equal #heads and tails)(f) * p(first heads appears on flip 4)(g) What is the probability either the first 3 flips or the last 3 flips are heads?(h) What does the previous problem suggest about p(EUF) for events E and F?

As per our guidelines we are suppose to answer only one question. Given,a coin is flipped once .

Answered: Experiment #1: Flipping a Coin. Assume…

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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Consider the given event. Two indistinguishable dice are rolled; the numbers facing up add to 9. How many elements are in the sample space S? n(S) = = 30 List the elements of the given event E. (Select all that apply.) (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) (2, 6), (3, 5), (4, 4) (3, 6), (4, 5) (1, 6), (2, 5), (3, 4) (1, 5), (2, 4), (3, 3) (1,4), (2, 3) Compute the probability of E. (Enter your probability as a fraction.) P(E) = 0.83 X
Consider the following experiment. A six-sided die is tossed twice and the number on the upper face is recorded for each toss. Define the simple events for the experiment. (Select all that apply.) O(2, 1) O(2, 2) O(2, 3) O(2, 4) O(2, 5) O(2, 6) O(2, 7) O(2, 8) O(1, 1) O(1, 2) O(1, 3) O(1, 4) O(1, 5) O(1, 6) O(1, 7) O(1, 8) O(3, 1) O(3, 2) O(3, 3) O(3, 4) O(3, 5) O(3, 6) O(3, 7) O(3, 8) O(4, 1) O(4, 2) O(4, 3) O(4, 4) O(4, 5) O(4, 6) O(4, 7) O(4, 8) O(5, 1) O(5, 2) O(5, 3) O(5, 4) O(5, 5) O(5, 6) O(5, 7) O(5, 8) O(6, 1) O(6, 2) O(6, 3) O(6, 4) О(6, 5) O(6, 6) O(6, 7) O(6, 8) O(7, 1) O(7, 2) O(7, 3) O(7, 4) O(7, 5) O(7, 6) O(7, 7) O(7, 8) O(8, 1) O(8, 2) O(8, 3) O(8, 4) O(8, 5) O(8, 6) O(8, 7) O(8, 8)
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A с B AG BG CG DG D AB BB CB DB Blue AR BR CR DR Red A person spins both of the spinners below. (Assume they are equally sp 1. What is the sample space? AB AY BB BY CB CY DB DY 2. What is the size of the sample space? 3. What is the probability of spinning "Blue" or "C"? Yellow 4. What is the probability of spinning "Blue" and "C"? Blue Green dec
True or False: For a given experiment, it is possible to have two events A and B for which p(A) + p(B) > p(AUB). True False
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
1. In the experiment of tossing 3 coins, what is the probability of getting 3 heads? 2. The events x and y are mutually exclusive events. If P(x) = 0.4 and P(y) = 0.3, what is the probability of either x or y? What is the probability that neither x nor y will occur? %3D %3D 3. A student enrolled two math subjects: statistics and algebra. His chance of passing the statistics subject 0.65. His chance of passing algebra is 0.80 and his chance of passing both subjects is 0.50. What is the probability of passing at least one subject?
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.
A person observes which direction a car turns at a T-intersection and records an L for a left hand turn and an R for a right hand turn. He records his observations for the next two cars that enter the intersection. (a) What is the sample space for the chance experiment of which direction the next two cars will turn? (b) Let E be the event that the first car turns right. List the outcomes of E. (c) Compute P(E). (d) Let F be the event that at least one of the cars turns left. List the outcomes of F. (e) Compute P(F).
Compound Random experiment: Flip a penny, draw a marble from a bag containg 3 red, 5 orange, and 2 green marbles. Draw the tree diagram to represent this compound random experiment. List the sample space. Compute the probabilities for each of the atomic events of the sample space. Event A = { Red marble and head on a penny or green marble tail on penny} Event B = { orange or green marble and head or tail on the penny} Calculate: p(A), p(b), p(A union B), and finally determine if they are independent events.

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