Question

1. A jar contains four marbles: t hree red, one whit e. Two marbles are drawn w ith replacement.
(i.e. A marble is randomly selected, the color noted, the marble replaced in the jar, then a second
marble is drawn.)
a. List a sample space containing four outcomes.
b. List a sample space with sixteen outcomes.
c. Write the probability of each of the four outcomes in (a).
d. What are the probabilit ies of the outcomes in (b)?
e. What is t he probability the colors of the two marbles match?
f. What is the probabilit y the same marble is draw n twice?

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Suppose R denotes a red marble, and W a white marble. This random experiment has four possibilities: RR, RW, WR, WW

P(R) =3/4 & P(W) = 1/4

Since the marbles are drawn with replacements,

P(RR) = (3/4) * (3/4) = 9/16

P(RW) = (3/4) * (1/4) = 3/16

P(WR) = (1/4) * (134) = 3/16

P(WW) = (1/4) * (1/4) = 1/16

We need to find probability of event consisting of (RR,WW) = 9/16 + 1/16 = 10/16 = 5/8