A fair six-sided die is rolled repeatedly. Show that a run of three consecutive sixes eventu- ally occurs with probability one.

Q: A faire dice is tussed twice Find the Probability that the two faces are the same CLEAR

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Q: Find the probability of scoring a total of 9 points in 2 tosses of a pair of fair dice (a) once, (b)…

A: We toss a dice 2 times. There are total 6 faces of a die. 1,2,3,4,5,6 Then number of times the total…

Q: If a coin is tossed 6 times. Calculate the probability of obtaining more tails than heads.

A: Given data: The number of times a coin is tossed n=6. The probability of getting the tail is, p=12…

Q: Suppose you roll two fair dice, one that is red and other is blue. Each die can have numbers from 1…

A: The total number of possible outcomes for rolling two fair dice is 36. The possible outcomes for…

Q: A die is rolled five times. A 4 is considered “success" ,while all other outcomes are "failures”…

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Q: If two cards are selected from a standard deck of 52 cards and are not replaced after each draw,…

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Q: uppose a jar contains 15 red marbles and 15 blue marbles. If you reach in the jar and pull out 2…

A: Number of red marbles=15Number of blue marbles=15Total number of marbles=30

Q: In a class with 50 students, 25 students constantly have their lunch in the cafeteria and 10…

A: Consider A denotes having lunch in the cafeteria and B denotes having lunch in the canteen.

Q: A fair coin is tossed 3 times. Find the probability of tossing 3 tails in a row,  answer as a…

A: Let H denote heads Let T denote tails Let S be sample set   S={ HHH, HHT, HTH, THH,       TTT, TTH,…

Q: We roll 5 six-sided die. What is the probability of obtaining exactly two 1s?

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Q: Find the probability of scoring a total of 8 points in 2 tosses of a pair of fair dice (a) once, (b)…

A: If a pair of fair dice is thrown then total number of outcomes, n(S) = 6*6 = 36 The event space for…

Q: ability of getting "six" at

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Q: Suppose we roll a pair of fair dice once. What is the probability of obtaining a 3 on a die 1 and a…

A: Suppose roll a pair of fair dice once. Then sample space S is   S=(1,1) (1,2)(1,3) (1,4) (1,5)…

Q: Packets at a certain node on the internet arrive with a rate of 100 packets per minute.Find the…

A: The arrival rate is 100 packets per minute that means 10010=10 packet per 6 seconds. The probability…

Q: A card is drawn at random from a deck of cards, find the probability of getting a Face Card (or Ace…

A: A card is drawn from a classical deck of cards. Thus, total possible outcomes=52 Define the events…

Q: You roll two dice at a time and not emultiple of those roll. What is probability that the outcome is…

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Q: If you roll a die twice, what is the probability that you get two sixes in a row?

A: Obtain the probability that you get two sixes in a row. The probability that you get two sixes in a…

Q: pitcher contains 3 red and 2 black marbles. You select two marbles without replacement. What is the…

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Q: Three balls are selected randomly from a bag containing 4 red balls and 7 blue ones. Find the…

A: From the provided information, Red balls = 4 Blue balls = 7 Total balls = 11

Q: Two pair of dice are rolled. What is the probability that the sum of their faces will be equal to…

A: Given: Two pair of dice are rolled. To find : The probability that the sum of their faces will be…

Q: Two dice are thrown simultaneously.Find the probability that the number of spots upper host is 9 or…

A: When two dice are thrown, there are 6*6 = 36 outcomes.

Q: A tennis player makes a successful first serve 40% of the time. Assume that each serve is…

A: The objective of this question is to find the probability of a specific outcome in a binomial…

Q: A bag has 12 different-colored marbles: 4 green, 5 blue, 1 yellow, and 2 orange. You draw a marble…

A: Given that,  4 green, 5 blue, 1 yellow, and 2 orange Marbles.  Total number of marbles = 4+5+1+2 =…

Q: coin is tossed 6 times. Find the probability of getting at least 1 tail.

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Q: If two dice are rolled one time, find the probability of getting a sum less than 9.5

A: We want to find the probability

Q: If two dice are rolled, find the probability that neither die shows a 5 on it. Probability

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Q: When a single die is tossed, what is the probability of getting a number that is a multiple of 2?

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Q: A tennis player makes a successful first serve 30% of the time. If she serves 33 times, what is the…

A: Solution: Let X be the number of first serves and n be the number of times she serves. From the…

Q: SHOW COMPLETE SOLUTION. If 30% of the bolts produced by a machine are defective, determine the…

A: Given,n=4p=0.3q=1-0.3=0.7A random variable X~Binomial(n=4 , p=0.3)P(X=x)=4x0.3x0.74-x  ;…

Q: A bag of multicolored balls contains 3 yellow, 4 blue, 1 black and 5 pink balls. If 3 balls are…

A: A bag of multicolored balls contains 3 yellow (3Y) 4 blue (4B) 1 black and  5 pink balls (5P) Total…

Q: A faire dice is tossed twice -11 LI Pace

A: Given, a fair dice is tossed twice.

Q: Assume you are rolling a die to see if a 6 appears in the first two rolls. True or false: the…

A: The probability of getting a six when a die is rolled = 16   The probability of getting a six for a…

Q: Two dice are thrown 5 times. If getting a doublet is a success. Find the probability that getting…

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Q: Find the probability that among 7 randomly chosen guests at a party no two share a birth month.

A: Given Data: The number of chosen guests is: N=7 The total number of the month (M) is 12. The total…