[An illustration of a jar of marbles is shown. Four of the marbles are labeled with...

[An illustration of a jar of marbles is shown. Four of the marbles are labeled with an upper R, seven of the marbles are labeled with an upper B, and five of the marbles are labeled with an upper G. The key identifies upper R to represent red marbles, upper B to represent blue marbles, and upper G to represent green marbles.]

a. What is the probability of selecting a red marble, replacing it, and then selecting a blue marble? Show your work.
b. What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? Show your work.
c. Are the answers to parts (a) and (b) the same? Why or why not?

Solutions

Expert Solution

Total number of marbles = 4 + 7 + 5 = 16

a) P(selecting a red marble, replacing it, and then selecting a blue marble) = 4/16 x 7/16

= 7/64

b) P(selecting a red marble, setting it aside, and then selecting a blue) = 4/16 x 7/15

= 7/60

c) The answers are not the same. In part (b), when the second marble is taken, the number of marbles from which we take the second one is 15. This is because we did not replace the first marble. So, the probability changes.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

(4) An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}.Four marbles...

(4) An urn contains 7 red marbles labeled {1,2,3,4,5,6,7} and 5 green marbles labeled {1,2,3,4,5}.Four marbles are pulled out at once (i.e. with no particular order). What is the probability that ... (a) ... all four marbles are red? (b) ... more of the marbles are green than red? (c) ... both red and green marbles are present? (d) ... two of the marbles chosen are both labeled "5"?

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 =

There are 10 marbles in a jar. They are identical except for color. Four are Red,...

There are 10 marbles in a jar. They are identical except for color. Four are Red, three are Blue, two are Yellow and one is White. You draw a marble from the jar, note its color, and set it aside. Then, you draw another marble from the jar and note its color. a) What is the probability that you draw two Red marbles? b) What is the probability that you draw a Blue marble GIVEN that you have drawn a...

You have a jar that contains 4 pink marbles, 3 yellow marbles,and 5 gray marbles....

You have a jar that contains 4 pink marbles, 3 yellow marbles, and 5 gray marbles.You will take out a marble at random and then replace it. You will do this a total of8 times.(a) Given that you observe at least 6 pink marbles, what is the probability that youobserve 1 yellow marble and 1 gray marble?

Harris and Mya each have a jar that contains 6 marbles. In each jar, d of...

Harris and Mya each have a jar that contains 6 marbles. In each jar, d of the marbles are blue and the remaining marbles are green. Harris will take out a marble from his jar at random and then replace it. He will then take out another marble from his jar at random and replaces it. Mya will take out two marbles from her jar at random without replacement. The probability that Mya observes two blue marbles is 80% of...

A jar contains 4 Orange, 3 Blue, and 2 Green marbles. (a) Two marbles are selected...

A jar contains 4 Orange, 3 Blue, and 2 Green marbles. (a) Two marbles are selected one at a time at random without replacement, so order is observed in the sample. Define the events:A=“the first marble is Orange”, B= “the second marble is Orange”. Find(i)P(A), (ii)P(B), (iii)P(A∪B) =P(at least one Orange marble is obtained in the 2 draws). Show your work. (b) Suppose instead three marbles are chosen at random from the jar by choosing 3 in one hand; no...

Suppose we draw 3 marbles from a jar containing 7 red and 5 blue marbles. At...

Suppose we draw 3 marbles from a jar containing 7 red and 5 blue marbles. At each stage, a ball is drawn and its color noted. Then the marble is returned to the jar along with another two marbles of the same color. Given that the ﬁrst marble is red, what is the probability that the next two are blue?

You draw marbles from a jar containing 5 black and 95 grey marbles. Let X be...

You draw marbles from a jar containing 5 black and 95 grey marbles. Let X be the number of drawings (with replacement) it takes until you get your first black marble. Let Y be the number of drawings (with replacement) it takes until you get your fifth black marble. Let Z be the number of black marbles removed if you draw 10 marbles without replacement. Calculate E[X] , Calculate P (Y = 90) ,Calculate Var(Z).

Suppose an opaque jar contains 3 red marbles and 10 green marbles. The following exercise refers...

Suppose an opaque jar contains 3 red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first one. What is the probability of getting a green marble first and a red marble second?

A jar contains 42 red marbles numbered 1 to 42 and 30 blue marbles numbered 1...

A jar contains 42 red marbles numbered 1 to 42 and 30 blue marbles numbered 1 to 30. A marble is drawn at random from the jar. Find the probability of the given event. Please enter reduced fractions. (a) The marble is red. P(red)= (b) The marble is odd-numbered. P(odd)= (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =

Subjects