Probability: if the omega - {A,B,C} is the sample space for an experiment then P({A}) =...

Question

Question

Probability:

if the omega - {A,B,C} is the sample space for an experiment then P({A}) = 1/3 (True or False?) explain.

if the omega - {A,B,C} is the sample space for an experiment, then P({A,B}) = 1 (True or False?) explain.

if a coin is tossed three times (and it is a fair coin) then the probability that H and T each come up at least once is 3/4 (True or False?) explain.

Answer 1

Answer #1

if the omega - {A,B,C} is the sample space for an experiment then P({A}) = 1/3

This is a false statement.

As there nowhere is written that all the three probabilities should be equal.

if the omega - {A,B,C} is the sample space for an experiment, then P({A,B}) = 1

This is a false statement.

As there nowhere is written that A and B always occur together

if a coin is tossed three times (and it is a fair coin) then the probability that H and T each come up at least once is 3/4

The statement is true

There are 8 possibilities in total and there are only two cases where only head {HHH} or only tails {TTT} occurs.

6 possibilities are there with atleast one head and tails.

probability = 6/8 = 3/4

Answer 2

Similar Homework Help Questions

a fair coin is tossed three times. A. give the sample space B. find the probability...

a fair coin is tossed three times. A. give the sample space B. find the probability exactly two heads are tossed C. Find the probability all three tosses are heads given that the last toss is heads
This is discrete mathematics If you do it right, I must give praise. You must use probability spa...

This is discrete mathematics If you do it right, I must give praise. You must use probability space is a triple relative acknowledge. S: is a sample sapce E=p(s) is the set of all events P: E-->R is a function. The important thing that I need to say three times: If you don't know how to do it, please don't do it. don't copy others, especially for question (a), give sample space, probability measure The important thing that I need...
4 PROBABILITY (16) An experiment consists of tossing a fair coin (head and tail T) three...

4 PROBABILITY (16) An experiment consists of tossing a fair coin (head and tail T) three times. The sample space S in this experiment is S - (HT), and a possible event Ecould be E = {H,H). (1) True. (2) False (17) Which of the following statements is true? (1) The set of all possible events of an experiment is called the sample space, S. (2) If an experiment is performed more than once, one and only one event can...

a coin is tossed three times. write the sample space for all the outcomes.calculate the probability...

a coin is tossed three times. write the sample space for all the outcomes.calculate the probability that the coin lands on heads at least two of those three times. show work, and write decimal to three decimal places.
1. A fair coin is tossed three times. Let A be the event that there are...

1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]
1. A fair coin is tossed three times. Let A be the event that there are...

1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]

An experiment consists of tossing a fair coin (head H, and tail T) three times. The...

An experiment consists of tossing a fair coin (head H, and tail T) three times. The sample space S in this experiment is S = {H, T}, and a possible event E could be E = {H,H}. (1) True. (2) False.
(2) What is the sample space you obtain if a fair coin and a die are...

(2) What is the sample space you obtain if a fair coin and a die are tossed? (3) Suppose there is a machine which randomly selects two digits from a collection of , 2, a. What are the sample points contained in the event that the sum of the two digits b. What are the sample points contained in the event that the absolute difference (4) Suppose that vehicles taking a particular freeway exit can turn right (R), turn left...
1. A fair coin is tossed three times. Let A be the event that there are...

1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? (5) c. Compute P(A), P(B), P(A|B), and P(BA). [7] 2. Let U be a continuous random variable with...

all questions please 1. (a) What is the sample space S for flipping a coin until...

all questions please 1. (a) What is the sample space S for flipping a coin until you get a head or 4 consecutive tails? Write down your sample space by listing the elements (b) An experiment involves tossing a pair of dice, one green and one red, recording the numbers that come up. These are special dice. Each die has only 5 sides and are labeled with the numbers 1, 2, 3, 4, 5. Let r be the outcome on...