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Data Analysis, Statistics, and Probability

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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