Question

In: Math

3. A box contains 5 red balls, 3 blue balls and 1 black balls. Take two...

3. A box contains 5 red balls, 3 blue balls and 1 black balls. Take two balls out randomly. Let X be number of red balls and Y be the number of black balls.

(1) Find the joint distribution of (X, Y ).

(2) Find P(X = 1|Y = 1).

Solutions

Expert Solution


Related Solutions

1).A box contains 20 balls. Five are blue, seven are red, and eight are black. Four...
1).A box contains 20 balls. Five are blue, seven are red, and eight are black. Four balls are selected at random and with replacement. Calculate the probability that fewer than two red balls are chosen. ANSWER: .5630 2. A company recently hired 50 employees. You are given: (a) Thirty employees are from Iowa; the remaining came from New York. (b) Of the employees who are from Iowa, 30% are males and the remaining are females. (c) Of the employees who...
Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box 2 contains...
Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box 2 contains 5 red balls, 3 green balls and 1 white ball. One ball of unknown color is transferred from Box 1 to Box 2. (a) What is the probability that a ball drawn at random from Box 2 is green? (b) What is the probability that a ball drawn from Box 1 is not white?
1) An urn contains 10 balls, 2 red, 5 blue, and 3 green balls. Take out...
1) An urn contains 10 balls, 2 red, 5 blue, and 3 green balls. Take out 3 balls at a random, without replacement. You win $2 for each green ball you select and lose $3 for each red ball you select. Let the random variable X denote the amount you win, determine the probability mass function of X. 2) Each of the 60 students in a class belongs to exactly one of the three groups A,B, or C. The membership...
(11 marks) In a box of 5 balls, 2 are red and 3 are blue. Two...
In a box of 5 balls, 2 are red and 3 are blue. Two balls are randomly selected (without replacement). Let X be the number of red balls in the two selected balls. a. Find the probability distribution of X (i.e., list all possible values of X and their corresponding probabilities). b. Find the expected value and the standard deviation of X.
An urn contains 5 red balls and 5 blue balls. ​(a) If 3 balls are selected...
An urn contains 5 red balls and 5 blue balls. ​(a) If 3 balls are selected all at​ once, what is the probability that 2 are blue and 1 is​ red? ​(b) If 3 balls are selected by pulling out a​ ball, noting its​ color, and putting it back in the urn before the next​ section, what is the probability that only the first and third balls drawn are​ blue? ​ (c) If 3 balls are selected one at a...
An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball,...
An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball, and a player is to draw one ball. If it is black, he wins $1, if it is red, he wins $2, if it is white he wins $3 and if it is blue, he pay $25. a. Set up the empirical probability distribution for the random variable X, the payoff of the game. Game Payoff (X) Probability [P(X) $1 $2 $3 $4 b....
Box A contains 6 red balls and 3 green balls, whereas box B contains 3 red...
Box A contains 6 red balls and 3 green balls, whereas box B contains 3 red ball and 15 green balls. Stage one. One box is selected at random in such a way that box A is selected with probability 1/5 and box B is selected with probability 4/5. Stage two. Finally, suppose that two balls are selected at random with replacement from the box selected at stage one. g) What is the probability that both balls are red? h)...
A box contains three white balls, two black balls, and one red ball. Three balls are...
A box contains three white balls, two black balls, and one red ball. Three balls are drawn at random without replacement. Let Y1 be the number of white balls drawn, and Y2 the number of black balls drawn. Find the distribution of Z = Y1 × Y2
A box contains 8 red balls, 4 green balls, and 3 blue balls. You pull 2...
A box contains 8 red balls, 4 green balls, and 3 blue balls. You pull 2 balls from the box (one at a time) WITHOUT replacement. **LEAVE ALL ANSWERS AS FRACTIONS** Find the probability of the following: a.) P(Red on 1st ball AND Red on 2nd ball) = b.) P(Green on 1st ball AND Red on 2nd ball) = c.) P(Blue on 1st ball AND Green on 2nd ball) = d.) What is the probability of drawing 2 green balls...
An urn contains 5 red, 3 orange, and 2 blue balls. Two balls are randomly selected...
An urn contains 5 red, 3 orange, and 2 blue balls. Two balls are randomly selected simultaneously. (a) What is the sample space? (b) Define an RV X as the number of orange balls selected. Show the map from the sample space to X. (c) Find the PMF of X. (d) Find the CDF of X. i have the solutions can one show how to find the probablity on 4c
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT