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# SAT Counting and Probability

In a box there are red, green, and blue marbles. One marble is selected at a time, and then placed back in the box. If the probability of selecting a red marble in this way is $$\frac{1}{8}$$ and the probability of selecting a green marble is $$\frac{13}{16},$$ what is the probability of selecting a blue marble?

(A) $$\ \ \frac{1}{8}$$

(B) $$\ \ \frac{1}{16}$$

(C) $$\ \ \frac{2}{3}$$

(D) $$\ \ \frac{7}{8}$$

(E) $$\ \ 1$$

An old man has $$63$$ children, grand- and great-grand children. What is the probability that at least $$6$$ of them are born in the same month?

(A) $$\ \ \frac{1}{63}$$

(B) $$\ \ \frac{3}{63}$$

(C) $$\ \ \frac{1}{60}$$

(D) $$\ \ \frac{1}{3}$$

(E) $$\ \ 1$$

A die is to be painted using two different colors, one for the dots, and one for the space between the dots. If there are $$11$$ available colors, in how many different ways can the die be painted?

(A) $$\ \ 11$$
(B) $$\ \ 21$$
(C) $$\ \ 55$$
(D) $$\ \ 110$$
(E) $$\ \ 121$$


As shown in the figure above, a circular dart board is made of two circles, one with radius $$r=6$$ and one with radius $$R=11.$$ If a dart is equally likely to land on any point on the board, what is the probability the dart will land in the shaded region?

(A) $$\ \ \frac{36}{121}$$

(B) $$\ \ \frac{85}{121}$$

(C) $$\ \ \frac{6}{11}$$

(D) $$\ \ 1$$

(E) $$\ \ \frac{36}{121}\pi$$

If a fair coin has already been tossed $$8$$ times, what is the probability that the $$9\text{th}$$ toss will result in tails?

(A) $$\ \ \frac{1}{2}$$

(B) $$\ \ \frac{1}{4}$$

(C) $$\ \ \frac{1}{8}$$

(D) $$\ \ \frac{1}{9}$$

(E) $$\ \ \left(\frac{1}{2}\right)^{9}$$

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