Three pens are drawn at random one at a time, without replacement, froma box containing 4 red pens and 6 black pens, where there is no outwarddifference visible between the different colours of the pens when making thechoice.If X is the random variable 'the number of red pens drawn',(a) Fill in the probability distribution for X in the table.0 1 23XP(X = x)Work out(b) the expected number of red pens E(X)(c) the standard deviation of X.

Here, there are 4 red pens and 6 black pens. Thus, the total there are 10 pens. The probability of…

Answered: Three pens are drawn at random one at a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A college tennis team has 15 players; 7 are seniorS, 3 are juniors, and 5 are sophomores. Two players are randomly selected to serve as captains for the next tournament. What is the probability that both players selected are seniors? The probability is (Round to four decimal places as needed.)
In a factory, there were 36 accidents involving machinery in the last six months. (a) Calculate the probability that there will be more than 2 accidents in the factory during the next months.
A sample of water has a 10% chance of containing a organic pollutant Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that the next 18 samples (i) exactly 3 contain the pollutant. (ii) at least two samples contain the gollutant.
When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 10% of the wells had neither impurity, 90% had impurity A, and 20% had impurity B. (Obviously, some had both impurities.) If a well is randomly chosen from those in the county, find the probability distribution for Y, the number of impurities found in the well. P(no impurities)= P(exactly one impurity)= P(both impurities)=
The probability that a person in the United States has type B+ blood is 8%. Five unrelated people in the United States are selected at random. Complete parts (a) through (d). (a) Find the probability that all five have type B+ blood. The probability that all five have type B+ blood is nothing. (Round to six decimal places as needed.) (b) Find the probability that none of the five have type B+ blood. The probability that none of the five have type B+ blood is nothing. (Round to three decimal places as needed.) (c) Find the probability that at least one of the five has type B+ blood. The probability that at least one of the five has type B+ blood is nothing. (Round to three decimal places as needed.) (d) Which of the events can be considered unusual? Explain. Select all that apply. A. The event in part (a) is unusual because its probability is less than or equal to 0.05. B. The event in part (b) is unusual because its probability is…
A group of botanists is studying the distribution of carnations in a field. The field is divided into a number of equal sized squares. The mean number of carnations per square is assumed to be 3. The carnations are distributed randomly throughout the field. Find the probability that: (b) (i) there will be more than two carnations. (ii) either five or six carnations.
In a game of blackjack played with one deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. A winning blackjack hand is won by getting 1 of the 4 aces, and 1 of 16 other cards worth ten points The two cards can be in any order. Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?
Suppose a dresser drawer has blue shirts, yellow shirts, red shirts, and green shirts so that if a shirt is pulled from the drawer at random, each color has an equal chance of being drawn. P(Green) = P(Blue) = P(Red) = P(Yellow) = ¼. Complete parts (a) – (d) to create a probability distribution for the number of yellow shirts if two shirts are pulled from the drawer at random (replacing the shirt after each draw). a. List each possible outcome for the colors of the shirts if two shirts are drawn randomly from the drawer. The teacher said there should be total of 16 outcomes, not 9 or 10. In my original answer, I have 10 outcomes when there should be 16. c.Find the probability of each event (not the probability from each outcome) from part (b). For my first answer, I had the probability of each outcome, and I should have the probability of each event.
Sneakers are no longer just for the young. In fact, most adults own multiple pairs of sneakers. Table gives the fraction of US adults 20 years of age and older who own five or more pairs of wearable sneakers, along with the fraction of the US adult population 20 years or older in each of five age groups. (1) Find the probability that the person owned at least five pairs of wearable sneakers. (2) Find the probability that the person selected was 65 years of age or older, given that the person owned at least five pairs of wearable sneakers. Groups and Ages G1 (20-24) G2 (25-34) G3 (35-49) G4 (50-64) G5 (≥65) Fraction with ≥ 5 pairs 0.26 0.2 0.13 0.18 0.14 Fraction of US Adult 20 and Older 0.09 0.18 0.3 0.25 0.18
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A market researcher wants to determine whether a new model of a personal computer that had been advertised on a late-night talk show had achieved more brand-name recognition among people who watched the show regularly than among people who did not. After conducting a survey, it was found that 12% of all people both watched the show regularly and could correctly identify the product. Also, 13% of all people regularly watched the show and 39% of all people could correctly identify the product. Define a pair of random variables as shown below. Complete parts (a) through (c). X=1 if regularly watch the show Y=1 if product correctly identified a. Find the joint probability function of X and Y X 0 1 (Do not round.) 0 X=0 otherwise Y=0 otherwise 1 CLLL 2 xdex ram

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