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Chapter 1: Q3SE (page 1)
Suppose that a certain precinct contains 350 voters, of which 250 are Democrats and 100 are Republicans. If 30 voters are chosen at random from the precinct, what is the probability that exactly 18 Democrats will be selected?
The probability of exactly 18 Democrats will be selected is 0.0579
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A box contains 24 light bulbs, of which two are defective. If a person selects 10 bulbs at random, without replacement, what is the probability that both defective bulbs will be selected?
Suppose that two boys named Davis, three boys named Jones, and four boys named Smith are seated at random in a row containing nine seats. What is the probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats?
Three pollsters will canvas a neighborhood with 21 houses. Each pollster will visit seven of the houses. How many different assignments of pollsters to houses are possible?
Suppose that 35 people are divided in a random manner into two teams in such a way that one team contains10 people and the other team contains 25 people. What is the probability that two particular people A and B will be on the same team?
Suppose that a number x is to be selected from the real line S, and let A, B, and C be the events represented by the following subsets of S, where the notation\(\left\{ {x: - - - - - } \right\}\)denotes the set containing every point x for which the property presented following the colon is satisfied:
\(\begin{aligned}{}{\bf{A = }}\left\{ {{\bf{x:1}} \le {\bf{x}} \le {\bf{5}}} \right\}\\{\bf{B = }}\left\{ {{\bf{x:3 < x}} \le {\bf{7}}} \right\}\\{\bf{C = }}\left\{ {{\bf{x:x}} \le {\bf{0}}} \right\}\end{aligned}\)
Describe each of the following events as a set of real numbers:
\(\begin{aligned}{l}{\bf{a}}{\bf{.}}\;{{\bf{A}}^{\bf{c}}}\\{\bf{b}}{\bf{.}}\;{\bf{A}} \cup {\bf{B}}\\{\bf{c}}{\bf{.}}\;{\bf{B}} \cap {{\bf{C}}^{\bf{c}}}\\{\bf{d}}{\bf{.}}\;{{\bf{A}}^{\bf{c}}} \cap {{\bf{B}}^{\bf{c}}} \cap {{\bf{C}}^{\bf{c}}}\\{\bf{e}}{\bf{.}}\;\left( {{\bf{A}} \cup {\bf{B}}} \right) \cap {\bf{C}}\end{aligned}\)
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