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

Q: Assume that there is a 9% rate of disk drive failure in a year. a. If all your computer data is…

A: Using basic concept of probability solve the above questions.

Q: A manufacturer uses electrical fuses in an electronic system. The fuses are purchased in large lots…

A:

Q: Find the probability of obtaining 2 ones, 1 two, 1 three, 2 fours, 3 fives, and 1 six in 10rolls of…

A: Solution

Q: A fair die with 6 sides is rolled 3 times, and every time it lands on a 4. Find the probability…

A: Introduction: The given die is fair and has 6 sides. Thus, the probability of each possible outcome,…

Q: Assuming that girl-boy births are equally probable, find the probability that a family with five…

A:

Q: Suppose that 20% of the programs sold at the home game of a professional sports team contain a…

A: Since, we have to calculate the probability that at least half of the friends received the discount…

Q: If a fair coin is tossed at random five independent times, find the conditional probability of five…

A: Given: Probability of Head in one coin p(H)=12. We have to find the conditional probability of coin…

Q: Consider an experiment of rolli: ollowing two events are indepe • Probability that the sum •…

A: The number of rolled dice are 3.

Q: If two coins are flipped once, what is the probability that both coins will turn up heads? Assume…

A: From the provided information, Two coins are flipped once. The coins are fair and head or tail is…

Q: We will toss a fair 6-sided die repeatedyl and let X denote the number of 5s that we roll. What is…

A: This problem can be solved using Binomial distribution

Q: Assume that there is a 11​% rate of disk drive failure in a year.   a. If all your computer data is…

A: Define the event F that the disk drive fails and event W is defined as the disk drive works. The…

Q: If you roll a fair 7-sided die 6 times, what is the probability hat a 6 is rolled at least twice?

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Q: Assume that there is a 5​% rate of disk drive failure in a year.   a. If all your computer data is…

A: Define the event F that the disk drive fails and event W is defined as the disk drive works. The…

Q: We will toss a fair 6-sided die repeatedyl and let X denote the number of 5s that we roll.

A: A 6 sided die is tossed repeatedly where X denotes the number of 5s that we roll. The total number…

Q: A pair of fair dice is rolled. What is the probability that the number landing uppermost on the…

A:

Q: If you have two six-sided die each labelled one throgh six. Which set of independent events has a…

A: It is an important part of statistics. It is widely used.

Q: A fair coin is flipped six times. What is the probability that tails occurs exactly 6 times if it is…

A: Conditional rule:The formula for probability of A given B is,

Q: Assume that there is a 5% rate of disk drive failure in a year. a. If all your computer data is…

A: Let X represent the random variable p=1-0.05=0.95   a) n=2   X~ Binomial (2, 0.95)

Q: Assume that there is a 10​%rate of disk drive failure in a year.   a. If all your computer data is…

A: Given information: P(Failure) = 0.10

Q: A fair coin is flipped six times. What is the probability that heads occurs exactly 5 times if it is…

A: Here, fair coin is flipped. hence, p=0.5 and q=0.5.The probability that heads occurs exactly 5 times…

Q: A jar contains 5 fair coins and 7 biased coins. Each biased coin is three times as likely to show…

A: Bayes' Theorem: Let A1, A2, ... , An be n mutually exclusive and exhaustive events with P(Ai) > 0…

Q: Suppose we roll a 6-sided die twice, and let R be a point in the 2D-plane, where the first…

A: Suppose we roll a 6-sided die twice, and let R be a point in the 2D-plane, where the first…

Q: If you roll a fair 8-sided die 7 times, what is the probability that none of the rolls are 1's or…

A:

Q: A fair coin is flipped three times. What is the probability that at least two consecutive heads…

A: Coin is tossed 3 times

Q: Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 oranges,…

A: Probability is the chance they occurrence in the event. Combination is the possible arrangement of…

Q: In a weather report, it is reported that 3 days out of each week will rain. (a) Dalai In 8…

A: It is reported that 3 days out of each week , it will rain which means 4 days out of each week , it…

Q: if your roll a fair 9-sided die 9 times, what is the probability that a 6 is rolled at least twice?

A: Given: Number of side of the die is, n(s)=9. Number of times rolled is, n(r)=9. The objective is…

Q: (a) tenth free throw on his twelfth shot, (b) first free throw on his sixth shot?

A:

Q: Two regular 6-sided dice are tossed. Compute the probability that the sum of the pips on the upward…

A:

Q: If you roll a fair 6 sided die 9 times, what is the probability at least two of the rolls come up as…

A: Given: A fair dice is rolled 9 times. P(Getting a three)=16 P(Not getting a three)=56 P(exactly one…

Q: A pair of fair dice is rolled. What is the probability that the number landing uppermost on the…

A: We find the outcomes for sum=7 of the numbers landing uppermost (1,6) , (2,5) , (3,4) , (4,3) ,…

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: Find the probability of throwing a sum of 12 at least 6 times in 12 throws of a pair of fair dice.

A: We know that, There are 36 outcomes for throwing a pair of dice ; 1 of these has a sum of 12 ( 6,6…

Q: Assume that there is a 9% rate of disk drive failure in a year. a. If all your computer data is…

A: Given that, P=9%= 0.09

Q: Calculate the probability that in i consecutive rolls of the same die, a six is not rolled twice in…

A: We need to find here six is not rolled twice in row and a six is rolled on the last roll.

Q: Assume that there is a 66​% rate of disk drive failure in a year.   a. If all your computer data is…

A: Introduction: A catastrophe would be caused if all the hard disk drives available to a person fail…

Q: If an employee is selected at random, find the probability that the employee is a deli/bakery worker…

A: Here total  employees = 45 represented in table  Probability = Favorable / total

Q: at in five tosses of a fair die, a 3 will appear at least

A: a) Given: n = 5 The sample space of a die is 1,2, 3, 4, 5, 6 i.e. there are 6 total outcomes.    p =…

Q: Given that a biased dice, where each of number 1jand number 3 appears half times as often as any…

A: Given problem Given that We need to find the probability that an even number appears when we roll…

Q: Suppose a 5-sided fair die numbered from 1-5. Roll it twice assuming each roll is independent of…

A: Given that the sum=8 So the possible outcomes are= (3, 5), (5, 3) , (4, 4). So 3 outcomes give sum=8…

Q: Assuming that boy and girl babies are equally likely, find the probability that a family with three…

A: Conditional rule:The formula for probability of A given B is,

Q: Assume that there is a 9​% rate of disk drive failure in a year.   a. If all your computer data is…

A: Given that 9% rate of disk drive failure in  year. That is, fail = 9%= 9/100=0.09 (a) The objective…

Q: A pair of dice is rolled. What is the probability that the sum will come up to be an even number and…

A: Favourable outcome of getting an even sum on the two dice given that one of them is 6 is given by =…

Q: When a bit is transmitted, it is received in error with probability p. Assume that 10 bits are…

A: Each of the bit is considered to be independently transferred and has a constant probability of p of…

Q: A pair of dice is tossed 10 times, what is the probability of obtaining a total of 8 or 11 a)…

A:

Q: Two balls are drawn in succession out of a box containing 7 red and 7 white balls. Find the…

A:

Q: Suppose there were four red balls and three yellow balls in a box. Three balls are drawn from the…

A: there are 4 red and 3 yellow balls to find: PROBABILITY that one ball of each coloring is selected

Q: Find the probability that exactly four defectives are found

A: Given: A manufacturing process has 10% defective rate.  Random sample of 15 tubes

Q: A die is weighted in such a way that each of 2, 4, and 6 is twice as likely to come up as each of 1,…

A: It is given that the each of 2,4, 6 is twice as likely to come up as each of 1,3,5.