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Probability - cards

4. A hand of 5 cards contains 2 red cards and 3 black cards. Trish plays the following game: A card is drawn from the hand. If the card is red, the game stops immediately. If the card is black, this black card is set aside and a red card is put into the hand in its place. Then another card is drawn from the hand and the same pro

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3. There are 13 standard decks of cards. Each deck is shuffled, separately. The 13 decks are lined up in a row on the table. The top card is drawn from each deck. What is the probability that at least 3 cards of each suit are drawn?


1. There are 3 boxes. Each box contains several envelopes. Some envelopes have "you lose" written on them. The rest say "you win..." . However, of the ones that say "you win..." , some contain only a piece of paper saying "... nothing" . Each of the other contains a $5 bill. The first box contains 3 "lose" envelopes and 2 so-


Problem 4. Let X denote the number of boys in a family with four children. Pr(X > 3) is? a. 5/16 b. ¼ c. 11/16 d. 2/3 e. None of the above

Probability & Statistics : Chebychev Inequality

Suppose that a probability distribution has a mean 20 and standard deviation 3. The Chebychev inequality states that the probability that an outcome lies between 16 and 24 is: a. less than 7/16 b. at least 7/16 c. at most 1/4 d. at least 1/4 e. none of the above

Probability & Statistics : Outcome of Dice Rolls

Two people play a game. A single die is thrown. If the outcome is a 2 or a 3, then player A pays player B $6.00. How much should B pay A when a 1, 4, 5, or 6 is thrown so that A and B break even, on average, over many repititions of the game? a. $2.00 b. $8.00 c. $4.00 d. $6.00 e. None of the above

Probability & Statistics : Quartiles

The test scores of 30 students are listed Below. Find Q3; 31 41 45 48 52 55 56 56 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 85 87 90 92 95 99

Sets, Counting and Probability : Events

A light Bulb manufacturer tests a light bulb by letting it burn until it burns out. The experiment consists of observing how long (in hours) the light bulb burns. Let E be the event "the bulb lasts less than 100 hours", F be the event "the bulb lasts less than 50 hours",and G be the event "the bulb lasts more than 120 hours." T


P(8,5) = a. 5!/8! b. 8*7*6*5*4 c. 8*7*6*5 d. 8!/5!3!

Probability : Combinations of Three-Numbered Spinners

Given two spinners divided into three equal parts. The first spinner is numbered 1- 2- and 3. The second spinner is numbered 4 - 5 - and 6. a. If each spinner is spun once, what is the probability that the product of the two numbers spun is even? b. What is the probability that the sum of the two is even?

Probability : Selection Without Replacement

John randomly picks (without replacing) four marbles from a jar that contains 6 red and 4 blue marbles. Mary randomly picks three marbles from a jar that contains 3 red and 5 blue marbles. What is the probability that John picks more blue marbles than Mary?

Unbiased bits per flip

Hi I would appreciate if you could help me with this question. Q. A coin that comes up heads with probability 3/4 on each flip can be used to generate more unbiased bits per flip ( on average ) than a coin that comes up heads with probability 7/8. Is it TRUE or FALSE and How ? Thanks

Frequencies of Dice Roll Combinations and Probabilities of Dice Rolls

When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over. A. Why will some numbers come up more frequently than others? B. Each die has six sides numbered from 1 to 6. How many possible ways can a nu

Statistics z test probability

Packages from packing machine have a mass, which is normally distributed with mean 200g and standard deviation 2g. Find the probability that the package from the machine weighs a) less than 197g b) more than 200.5g (use standard normal variable Z and normal distribution tables)

Probability and proportion

Suppose that a market for a certain type of automobile consists of those made by manufacturers 1 and 2... what is the probability that at least 150 automobiles in the market lasts over 10 years? Please see attached.

Probability : Maximium Likelihood Estimator and p-Values

A GMAT test center reports that out of 200 students who took a GMAT test at the test center 60 scored above 600. a) Derive the maximum likelihood estimator (MLE) of p, the proportion of students scoring above 600. What is the ML estimate of n*p(1-p) b) What is the MLE of P(X<50)? c) Test if the proportion of students sc

Probability distribution

A single die is rolled once. You lose $12 if a number divisible by 3 turns up. How much should you win if a number not divisible by 3 turns up for the game to be fair? How would I set this up, and what formulas?

Probability : Sampling Without Replacement - Card Hands

6. A hand of 4 cards contains one card of each suit ( I,e., one Heart, one Diamond, One Club and one spade). Simon uses this hand to play a game for which the rules are as follows: (1) When a Heart is drawn, the game stops immediately. (2) If the Diamond is drawn, the Diamond is set aside and not replaced (so that when the game


Three friends play a game of darts until one of the 3 is declared a winner. It is known that Jan is twice as likely to win as Julio, and Jean is only half as likely to win as Julio. (a) What is the probability that Julio will win? (b) If Jan didn't win, what is the probability that Julio did?

Combinations and Probability (8 Problems) - Camp Cawapati

1. At Camp Cawapati, there is a prize ceremony at the end of each camp session. The campers compete at a variety of challenges throughout the 2-week session, in hopes of earning trophies. For each challenge a camper wins, the camper receives a small replica of the Sacred Cawapati Cup. (These replica trophies are all identical.)

Probabilities related to a sample mean.

The breaking strength of a rivet has a mean value of 10,000 psi and a standard deviation of 500 psi. a. What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9900 and 10,200. b. If the sample size had been 15 rather than 40, could the probability requested in part (a) b

Joint Probability Distribution Function

10. Annie and Alvie have agreed to meet between 5:00 pm and 6:00 pm for dinner at a local health food restaurant. Let X=Annie's arrival time and Y=Alvie's arrival time. Suppose X and Y are independent with each uniformly distributed on the interval [5, 6]. a. What is the joint pdf of X and Y? b. What is the probability that

Poisson Probability Distribution

80. Suppose that only .10% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 10,000 computers ... Please see attachment for complete question. Thanks

Quota, Banzhaf Distribution and Shapely-Shubick Distribution


Probability; Interest Rate; Bacteria Multiplication

PLEASE SHOW ALL WORK FOR COMPLETE UNDERSTANDING! 1) A bacteria culture starts with 7 bacteria which multiply simultaneously every three house. If the first generation is born fromt he initial group at 12 midnight a. How many bacteria will be in the culture at midnight the next night? b. Also what time will there be 224


Some parts of California are particularly earthquake-prone. Suppose that in one such area... a) Find the probability distribution of X... Please see attached.