There are three types of balls in a box: 5 red, 3 blue and 2 green....

There are three types of balls in a box: 5 red, 3 blue and 2 green. You draw 3 balls at once (without replacement) from this box and record: Y1=the # of red balls, Y2=the # of blue balls that you drew. Find the joint probability distribution of Y1, Y2, by first writing the possible values for y1, y2 in rows and columns and then filling in the probabilities within this table. Then check that the sum of the entries in the table equals 1.

Expert Solution

orchestra answered 1 year ago

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?

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...

There are 6 purple balls, 5 blue balls, and 3 green balls in a box. 5...

There are 6 purple balls, 5 blue balls, and 3 green balls in a box. 5 balls were randomly chosen (without replacing them). Find the probability that (a) Exactly 3 blue balls were chosen. (b) 2 purple balls, 1 blue ball, and 2 green balls were chosen.

(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.

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).

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...

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 2 ?red, 3 white and 3 green balls. Two balls are drawn out...

A box contains 2 ?red, 3 white and 3 green balls. Two balls are drawn out of the box in succession without replacement. What is the probability that both balls are the same? color?

3 red balls, 4 blue balls, and 3 green balls are randomly placed in a line....

3 red balls, 4 blue balls, and 3 green balls are randomly placed in a line. What is the probability that there is at least one red and at least one blue between each pair of green balls?

3. Box A contains 6 red balls and 3 green balls, whereas box B contains 3...

3. 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: First, suppose that 1 ball is selected at random from the box selected at stage one. a) What is the probability that the ball is red? b) Given that...

Question