Twelve marbles are placed in a hat, three are black, two blue, one green, four white...

Twelve marbles are placed in a hat, three are black, two blue, one green, four white and two red. Two marbles are drawn out at random, without replacement. Find the probability that

(a). Both marbles are black.

(b).one of them is red, and the other is green.

(c). Neither marble is white.

Expert Solution

orchestra answered 1 year ago

A bag contains one red marble, two blue marbles and three green marbles. A marble is...

A bag contains one red marble, two blue marbles and three green marbles. A marble is selected at random. Define a random variable X such that X=1 if a red marble is selected, X=2 if a blue marble is selected and X=3 if a green marble is selected. Find the following probabilities. Hint: The blue marbles are different; you can label one blue-1 and the other blue-2. Similarly, each of the green marbles is different. 4a) Find P(X=1) 4b) Find...

Suppose box 1 has four black marbles and two white marbles, and box 2 has two...

Suppose box 1 has four black marbles and two white marbles, and box 2 has two black marbles and five marbles. If you picked one marble from one of the two boxes at random, what it the probability that you picked from box 1 given that the marble you picked is black? A raffle has 5000 tickets with the following prizes: 1 ticket has $2000 prize, 10 tickets have $200 prize, and 20 tickets have $50 prize and 500 tickets...

An urn contains three blue and seven green marbles. Alice chooses two marbles at random from...

An urn contains three blue and seven green marbles. Alice chooses two marbles at random from the urn. If they have the same color, Bob will pay her $7; but if they have different colors, Alice will pay Bob $8 a) Give the probability distribution for Alice’s payoffs of this game. Use proper headings for the table. b) What are Alice expected winnings in this game? Is it a fair game?

A box contains 5 green marbles, 8 blue marbles, and 8 red marbles. Three marbles are...

A box contains 5 green marbles, 8 blue marbles, and 8 red marbles. Three marbles are selected at random from the box, one at a time, without replacement. Find the probability that the first two marbles selected are not red, and the last marble is red.

A bag contains four red marbles, two green ones, one lavender one, three yellows, and three...

A bag contains four red marbles, two green ones, one lavender one, three yellows, and three orange marbles. HINT [See Example 7.] How many sets of five marbles include at most one of the yellow ones?

13) A box contains 5 green marbles, 6 blue marbles, and 8 red marbles. Three marbles...

13) A box contains 5 green marbles, 6 blue marbles, and 8 red marbles. Three marbles are selected at random from the box, one at a time, without replacement. Find the probability that the first two marbles selected are not red, and the last marble is red. Round your answer to four decimal places.

An urn contains five black marbles and one orange marbles. Four marbles are drawn out one...

An urn contains five black marbles and one orange marbles. Four marbles are drawn out one at a time. For each marble, if it is black the marble is set aside, but if it is orange it is returned to the urn before the next marble is drawn. Let X be the number of black marbles drawn from the urn. Find the probability distribution for X and find the expectation value and variance of X

5. Max grabs three marbles from a bag containing five white marbles and six black marbles....

5. Max grabs three marbles from a bag containing five white marbles and six black marbles. What is the probability that exactly two of the marbles are black?

Assume jar has four red marbles and two black marbles. Draw out two marbles with and...

Assume jar has four red marbles and two black marbles. Draw out two marbles with and without replacement. Find the requested probabilities (enter the probabilities as fractions.) a.) p(two red marbles) with replacement = without replacement = b.) p(two black marbles) with replacement = without replacement = c.) p(one red and one black marble) with replacement = without replacement = d.) p(red on the first draw and black on the second draw) with replacement = without replacement =

A hat contains a number of cubes: 3 red, 2 white, 1 blue, and 4 black....

A hat contains a number of cubes: 3 red, 2 white, 1 blue, and 4 black. If one cube is chosen at random, what is the probability that it is: A red cube? (3 points) Not a red cube? (3 points) A cube that is white OR black? (4 points) A cube that is neither white nor black? (4 points) What do the answers to part a and part b add up to and why? (5 points) If three cubes...

Question