Show work! Suppose a hat contains eight marbles of two different colors. Four ar

Question

Show work!

Suppose a hat contains eight marbles of two different colors. Four are white and four are yellow. Assume all selections are made without replacement (the marble selected is not placed back in the hat).

Question 1:    What is the probability that three successive marbles selected will be white?

Question 2:    What is the probability that for three successive marbles selected, atleast one will be white?

Question 3:    What is the probability that for three successive marbles selected, two or more will be yellow?

Question 4:    Given that the first two marbles selected are yellow, what is the probability that the third marble selected will be white?

Question 5:    What is the probability that for four successive marbles selected, the colors of the marbles will alternate (no successive picks will be of the same color)?

Explanation / Answer

1) Probability that three successive white marbles are taken out:

= Probability that first marble drawn is white * Probability that second marble drawn is white given that first is white * Probability that third marble drawn is white given that first two are also white

= ( 4/ 8) * ( 3/7)* ( 2/6)

= 0.0714

Therefore 0.0714 is the required probability here.

2) Probability that out of three marbles drawn, at least one is white is computed as:

= 1 - Probability that none is white

= 1 - ( 4/ 8) * ( 3/7)* ( 2/6)

= 1 - 0.0714

= 0.9286

Therefore 0.9286 is the required probability here.

3) Probability that two or more will be yellow in the three marbles drawn

= Probability that exactly 2 are yellow + Probability that all 3 are yellow

= 3*( 4/ 8) * ( 3/7)* ( 4/6) + 0.0714

= 0.5000

Therefore 0.5000 is the required probability here.

4) Given that first two marbles drawn are yellow, probability that the third marble is white is computed here as:

= 4 / 6

= 0.6667

Therefore 0.6667 is the required probability here.

5) Now here, there are 2 possibilities, either WYWY or YWYW

The probability therefore here is computed as:

= 2*(4/8)*(4/7)*(3/6)*(3/5)

= 0.1714

Therefore 0.1714 is the required probability here.

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