A.) Which of the following events is most likely: At least one 6, when 6 fair...
A.) Which of the following events is most likely:
- At least one 6, when 6 fair die are rolled
- At least two 6's, when 12 fair die are rolled
- At least three 6's, when 18 fair die are rolled
- All have the same probability
B.) We have to events, A and B in the same sample space,
. If P(A) = 0.4 and P(B) = 0.65, the two events are disjoint. Is
this true or false?
Homework Answers
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A.) Which of the following events is most likely:
At least one 6, when 6 fair...
What is the most likely outcome when we throw two fair dice, i.e., what is the most likely sum th...
What is the most likely outcome when we throw two fair dice,
i.e., what is the most likely sum that the two dice would add to?
Why? This problem can be solved by first principles. The probability
P(E) for an event E is the ratio |E|/|S|, where |E| is the
cardinality of the event space and |S| is the cardinality of the
sample space. For example, when we throw a fair die, the event
space is S = {1,2,3,4,5,6} and...
A fair die is rolled and the following events are considered:
1) A fair die is rolled and the following events are considered: A is the event that the outcome is an even. B is the event that the outcome is no more than2. C is the event that the outcome is greater than or equal to 4. Answer the following questions: (a) List the sample space and events A, B and C. (b) Find P(A), P(B) ad P(C) (c) Are A and B independent? Show your work. (d) Are A and C independent? Show your work. (e) Find the...
1. We roll two fair 6-sided dice. Compute the probabilities of the following events. (a) The...
1. We roll two fair 6-sided dice. Compute the probabilities of the following events. (a) The sum is at most 6. (b) The sum is more than 6. (c) The sum is at most 6 and at least one die is a 4. 2. Consider the letters a,b,c. Suppose we draw 2 of the letters at random (allowing for repetition). Assume order matters. That is, ab is not the same as ba: Let A : The 2 letters are distinct....
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled...
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True or false with explanation please. 12 pts.True or false section(Write down BOTH QUESTION ANDANSWER at...
True or false with explanation please.
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Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is all...
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is allowed to bet on two sets of outcomes: A (1,2,3) and B (2,4,5,6). If he bets on A then he wins $1 if one of the numbers in A is rolled and otherwise he loses $1 -let X be the amount won by betting on A (so P(X-1)-P(X1)If he bets on B then he wins $0.50 if a number in...
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to...
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to be 1, 2, 3, 4, 5, 6, 7, or 8.) (a) What is the probability that at least one of the rolls is a 3? (b) Let X be the number of different values rolled. For example, if the five rolls are 2, 3, 8, 8, 7, then X = 4 (since four different values were rolled: 2,3,7,8). Find E[X].
When a fair die is rolled, it has equal chance to show one of six faces,...
When a fair die is rolled, it has equal chance to show one of six faces, labelled 1 through 6. If it is rolled 10 times, what is the probability that there are at least three 6's?
A fair 6-sided die rolled 5 times. what is the probability that at least one of...
A fair 6-sided die rolled 5 times. what is the probability that at least one of the rolls is 2
Conditional Probability Two fair dice are rolled: (a) Express the sample space S in set builder...
Conditional Probability Two fair dice are rolled: (a) Express the sample space S in set builder notation and the probability P "At least one of the dice rolls a four." Write all possible outcomes of A (b) Consider the event A (c) What is the probability that at least one die rolls a four? (d) What is the conditional probability that the first die rolls a four given that the sum of the dice is six? (e) What is the...
What is the most likely outcome when we throw two fair dice,
i.e., what is the most likely sum that the two dice would add to?
Why? This problem can be solved by first principles. The probability
P(E) for an event E is the ratio |E|/|S|, where |E| is the
cardinality of the event space and |S| is the cardinality of the
sample space. For example, when we throw a fair die, the event
space is S = {1,2,3,4,5,6} and...
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled twice. For example, "1,4" would indicate 1 was rolled first and then 4 was rolled second a) Write down the possible outcomes, i.e., the sample space. (b) List the outcomes in the following events: Event A: The number 4 came up zero times. Event B: The number 4 came up exactly one time. . Event C: The sum of the two rolls is odd...
True or false with explanation please.
12 pts.True or false section(Write down BOTH QUESTION ANDANSWER at your answer booklet DON'T GUESS You throw a dice and toss a coin simultaneously. The sample space of this experiment contains 8 different values. t 12 b. A CRV has uniform distribution from -4 to 8. Its variance is c. | The probability of a certain event is 1. d If A and B are two disjoint events, where PIA]-0.1 and PIBI-0.4 then PIA...
Question 3 (15 pts). A gambler plays a game in which a fair 6-sided die will be rolled. He is allowed to bet on two sets of outcomes: A (1,2,3) and B (2,4,5,6). If he bets on A then he wins $1 if one of the numbers in A is rolled and otherwise he loses $1 -let X be the amount won by betting on A (so P(X-1)-P(X1)If he bets on B then he wins $0.50 if a number in...
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Conditional Probability Two fair dice are rolled: (a) Express the sample space S in set builder notation and the probability P "At least one of the dice rolls a four." Write all possible outcomes of A (b) Consider the event A (c) What is the probability that at least one die rolls a four? (d) What is the conditional probability that the first die rolls a four given that the sum of the dice is six? (e) What is the...
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