![4. Exercise: Independence of two events -I A Bookmark this page Exercise: Independence of two events - I 1 point possible (graded) We have a peculiar coin. When tossed twice, the first toss results in Heads with probability 1/2. However, the second toss always yields the same result as the first toss. Thus, the only possible outcomes for a sequence of 2 tosses are HH and TT, and both have equal probabilities. Are the two events A Heads in the first toss and B Heads in the second toss] independent? Select an option Select an option Yes, they are independent attempt f 1 No, they are dependent Save](http://img.homeworklib.com/questions/b2864ed0-f40f-11eb-abaa-351475dec8e7.png?x-oss-process=image/resize,w_560)
Homework Answers
A peculiar coin is tossed two time.
The first toss results in Heads with probability 1/2.
Here it is also mentioned that the second toss always yields the same results as the first toss.
From the above condition we can say that events A (Heads in the first toss) and event B (Heads in the second toss) are dependent.
Answer: No, they are dependent.
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Ex 4 Independence of Two Events
4. Exercise: Independence of two events -I A Bookmark this...
A box contains five coins. For each coin there is a different probability that a head...
A box contains five coins. For each coin there is a different probability that a head will be obtained when the coin is tossed. (Some of the coins are not fair coins!) Let pi denote the probability of a head when the i th coin is tossed (i = 1, . . . , 5), and suppose that p1 = 0, p2 =1/4, p3 =1/2, p4 =3/4, p5 =1. The experiment we are interested in consists in selecting at random...
A coin will be tossed twice, and each toss will be recorded as heads ( H...
A coin will be tossed twice, and each toss will be recorded as heads ( H ) or tails ( T ). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the first toss is heads. Use the format HT to mean that the first toss is heads and the second is tails. If there is more than one element in the set, separate them with commas. Samplespace: Eventthatthefirsttossisheads:
A coin will be tossed twice, and each toss will be recorded asheads (H...
A coin will be tossed twice, and each toss will be recorded as heads (H) or tails (T).Give the sample space describing all possible outcomes.Then give all of the outcomes for the event that the second toss is tails.Use the formatHTto mean that the first toss is heads and the second is tails.If there is more than one element in the set, separate them with commas.
35. You and I play the following game: I toss a coin repeatedly. The coin is...
35. You and I play the following game: I toss a coin repeatedly. The coin is unfair and P(H) = p. The game ends the first time that two consecutive heads (HH) or two consec- utive tails (TT) are observed. I win if (HH) is observed and you win if (TT) is observed. Given that I won the game, find the probability that the first coin toss resulted in heads?
A coin is tossed three times. An outcome is represented by a string of the sort...
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails). The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions. (If necessary, consult a list of formulas.) (a) Check the outcomes for each of the three events below. Then, enter the probability of each event. (a) Check the outcomes for each...
4. Let 210,1,2) be the outcome space in a model for tossing a coin twice and...
4. Let 210,1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of Ω. If you say "yes," provide the subset; if you say "no," explain why: a) the coin does not land heads both times; bon one of the tosses the coin lands heads, and on the other toss it lands tails; Section 1.3. Distributions 31 C) on the...
1. Suppose that each child born to a couple is equally likely to be a boy...
1. Suppose that each child born to a couple is equally likely to be a boy or a girl, inde- pendently of the gender distribution of the other children in the family. For a couple having 5 children, compute the probabilities of the following events: (a) All children are of the same gender (b) The 3 eldest are boys and the others girls. (c) Exactly 3 are boys. (d) The 2 oldest are girls. e) There is at least 1...
Please give help for this question. Question 4. Coin tossing, again. In class on Monday, January...
Please give help for this question.
Question 4. Coin tossing, again. In class on Monday, January 29th, we discussed an example showing that the conditional independence of events does not imply their unconditional independence. As a reminder, the setup of the example was as follows. We had two coins, coin A and coin B. We chose a coin at random (i.e., with probability 0.5) and tossed the chosen coin repeatedly. Given the choice of a coin, the coin tosses were...
please show details 4. Let S2 (0, 1,2) be the outcome space in a model for...
please show details
4. Let S2 (0, 1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of 2. If you say "yes," provide the subset; if you say "no," explain why a) the coin does not land heads both times; b) on one of the tosses the coin lands heads, and on the other toss it lands tails; Section...
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...
35. You and I play the following game: I toss a coin repeatedly. The coin is unfair and P(H) = p. The game ends the first time that two consecutive heads (HH) or two consec- utive tails (TT) are observed. I win if (HH) is observed and you win if (TT) is observed. Given that I won the game, find the probability that the first coin toss resulted in heads?
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails). The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions. (If necessary, consult a list of formulas.) (a) Check the outcomes for each of the three events below. Then, enter the probability of each event. (a) Check the outcomes for each...
4. Let 210,1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of Ω. If you say "yes," provide the subset; if you say "no," explain why: a) the coin does not land heads both times; bon one of the tosses the coin lands heads, and on the other toss it lands tails; Section 1.3. Distributions 31 C) on the...
1. Suppose that each child born to a couple is equally likely to be a boy or a girl, inde- pendently of the gender distribution of the other children in the family. For a couple having 5 children, compute the probabilities of the following events: (a) All children are of the same gender (b) The 3 eldest are boys and the others girls. (c) Exactly 3 are boys. (d) The 2 oldest are girls. e) There is at least 1...
Please give help for this question.
Question 4. Coin tossing, again. In class on Monday, January 29th, we discussed an example showing that the conditional independence of events does not imply their unconditional independence. As a reminder, the setup of the example was as follows. We had two coins, coin A and coin B. We chose a coin at random (i.e., with probability 0.5) and tossed the chosen coin repeatedly. Given the choice of a coin, the coin tosses were...
please show details
4. Let S2 (0, 1,2) be the outcome space in a model for tossing a coin twice and observing the total number of heads. Say if the following events can be represented as subsets of 2. If you say "yes," provide the subset; if you say "no," explain why a) the coin does not land heads both times; b) on one of the tosses the coin lands heads, and on the other toss it lands tails; Section...
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...
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