4. Suppose a game consists of rolling a die 12 times independently. You win $1 each time the upface of the die is 2, 3, 5, or 6. Let X be the random variable that measures the gain of this game. (a) What is the probability of winning $0 in this game? (Z) (b) What (b) What is the probability of winning exactly $1 in this game? (c) What is the probability of gaining at least $1 in this game? (d) What is the expected gain of this game? (e) What is the variance of X? (10 Ad

Q: (2) Suppose you roll three fair dice. What is the probability that all three numbers are identical?…

A: Probability of an event=favourable outcomestotal outcomes

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A: A die is tossed one time,  The possible outcomes are{1,2,3,4,5,6}. Sample space, n(S)=6

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A:

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A: a) Assume an event A, defines the event of selecting heart.

Q: exact

A: Here use binomial distribution  Finite number of toss Each trial is independent from each other…

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Q: (i) Six dice are thrown 405 times. How many times do you expect to at least 5 dice to have a four or…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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A: Note: Thank you for the question. Since the question in part © is incomplete we have considered it…

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A: Answer is TRUE

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A: Note: Hey there! Thank you for the question. As you have posted multiple sub-parts, according to our…

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A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Suppose Nate wins 43% of all staring contests. (a) What is the probability that Nate wins two…

A: We have given that Probability of nate wins all starting contests P(wins) = 0.43 P(loose) = 1 - 0.43…

Q: (a) Find the probability of the event that two faces are the same without the information given. (b)…

A: The events E is defined as E = two faces are the same

Q: An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Find…

A: Sample space of rolling two dice: s=(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)…

Q: A pair of six-sided dice is rolled one time. What is the probability that the number 5 will appear?…

A:

Q: Two dice are rolled.  (a) write out a sample space (b) find the probability of getting a sum of 6 or…

A: Given that ; Two dice are rolled.  A dice contains 6 digits i.e. { 1,2,3,4,5,6} Here we use basic…

Q: oll a pair of dice 100 times. Keep a record of the sums of the dice. Find the theoretical…

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Q: Exercise 8. In a dice game, players each roll 6 fair 6-sided dice. Each player keeps track of the…

A: Given information: 6 fair 6-sided dice Let I be subject A and you be the subject B.

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A: Given Data:   A B C Total Male 12 19 9 40 Female 3 7 11 21 Total 15 26 20 61

Q: Example: 8AFind the probability of selecting 4 marbles from a bag of 3 red marbles and 7 blue…

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A: select three cards from 52 card deck.  we have to find probability of given events.

Q: 3. (a) You roll three fair six-sided dice. What is the probability that you obtain a total of (i) 5…

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Q: For a normal die, the sum of the dots on opposite faces is 7. Shown in the figure is a pair of trick…

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