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#1. Two 5-sided fair dice are thrown sequentially, and the face values that come up are...
Two fair (6-sided) dice are rolled. If you are told that the two dice end up...
Two fair (6-sided) dice are rolled. If you are told that the two dice end up with two different face values, what is the probability that one die has a face value of 6?
Two fair dice are tossed and the up face on each die is recorded. Find the...
Two fair dice are tossed and the up face on each die is recorded. Find the probability of observing each of the following events: A:{the difference of the numbers is 1} B:{the sum of the numbers is equal to one} C:{the sum of the numbers is even} P(A)= P(B)= P(C)=
3-(35 points) Two standard 6-sided dice with 6 faces having values (1,2,3,4,5,6) are thrown and the...
3-(35 points) Two standard 6-sided dice with 6 faces having values (1,2,3,4,5,6) are thrown and the face values on the top face of cach die are observed. Let E be the event that the maximum of the dice face values is odd Let F be the event that none of the dice lands on the value 1. Let G be the event that the product is less or equal to 6. a) Determine the probabilities of all events: E, F,...
Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded
Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded. Define the following events: E:{The sum of the numbers is even } F:{A6 on the blue die } Find the following probabilities:(a) P(E)=18 / 36(b) P(F)=4 / 36(c) P(E ∩ F)=Are events E and F independent?A. yesB. no
1. A pair of fair dice is thrown, what is the probability that the sum of...
.1. A pair of fair dice is thrown, what is the probability that the sum of the two numbers is greater than 10. 2. A pair of fair dice is thrown. Find the probability that the sum is 9 or greater if a. If a 6 appears on the first die. b. If a 6 appears on at least one of the dice.
1. Two fair dice are thrown and the smallest of the face values, Z say, is...
1. Two fair dice are thrown and the smallest of the face values, Z say, is noted (a) Give the probability mass function (pmf) of Z in table form: P(Z=2) (b) Calculate the expectation of 1/Z 2] (c) Consider the game, where a player throws two fair dice, and is paid Z dollars, with Z as above. To enter the game the player is required to pay 3 dollars What is the expected profit (or loss) of the player, if...
1. Two dices are thrown (a) List the elements of the sample space. (b) List the...
1. Two dices are thrown (a) List the elements of the sample space. (b) List the outcomes that define the following events. E: At least one of the dice rolls on 6. he same number . F: Both dice roll on t . G: The sum of the dice is odd H: The number on the first die is larger than the number on the second die. (c) Explain whether the following events are mutually exclusive or not (i) E...
Questions 1-7: Hector will roll two fair, six-sided dice at the same time. Let A =...
Questions 1-7: Hector will roll two fair, six-sided dice at the same time. Let A = the event that at least one die lands with the number 3 facing up. Let B = the event that the sum of the two dice is less than 5. 1. What is the correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5”? 2. Calculate the...
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled...
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...
Two six-sided dice will be rolled once and the numbers (number of dots) on each dice...
Two six-sided dice will be rolled once and the numbers (number of dots) on each dice is to be recorded. Define events Еґ the sum of the two dice is 1,1-2,3, , 12. a. List all the outcomes in the Sample Space. Calculate the probability of each event, El, E2, , E12. c. Let A be the event "the sum of the two dice is greater than 6" Calculate P(E10|A) and P(A|E10)
3-(35 points) Two standard 6-sided dice with 6 faces having values (1,2,3,4,5,6) are thrown and the face values on the top face of cach die are observed. Let E be the event that the maximum of the dice face values is odd Let F be the event that none of the dice lands on the value 1. Let G be the event that the product is less or equal to 6. a) Determine the probabilities of all events: E, F,...
1. Two fair dice are thrown and the smallest of the face values, Z say, is noted (a) Give the probability mass function (pmf) of Z in table form: P(Z=2) (b) Calculate the expectation of 1/Z 2] (c) Consider the game, where a player throws two fair dice, and is paid Z dollars, with Z as above. To enter the game the player is required to pay 3 dollars What is the expected profit (or loss) of the player, if...
1. Two dices are thrown (a) List the elements of the sample space. (b) List the outcomes that define the following events. E: At least one of the dice rolls on 6. he same number . F: Both dice roll on t . G: The sum of the dice is odd H: The number on the first die is larger than the number on the second die. (c) Explain whether the following events are mutually exclusive or not (i) E...
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...
Two six-sided dice will be rolled once and the numbers (number of dots) on each dice is to be recorded. Define events Еґ the sum of the two dice is 1,1-2,3, , 12. a. List all the outcomes in the Sample Space. Calculate the probability of each event, El, E2, , E12. c. Let A be the event "the sum of the two dice is greater than 6" Calculate P(E10|A) and P(A|E10)
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