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Chapter 1: Q10E (page 41)
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?
The probability that both defective bulbs will be selected is 0.16
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Suppose that one card is to be selected from a deck of 20 cards that contains 10 red cards numbered from 1 to 10 and 10 blue cards numbered from 1 to 10. Let A be the event that a card with an even number is selected, let B be the event that a blue card is selected, and let C be the event that a card with a number less than 5 is selected. Describe the sample space S and describe each of the following events both in words and as subsets of S:
a. \({\bf{A}} \cap {\bf{B}} \cap {\bf{C}}\)
b. \({\bf{B}} \cap {{\bf{C}}^{\bf{C}}}\)
c. \({\bf{A}} \cup {\bf{B}} \cup {\bf{C}}\)
d. \({\bf{A}} \cap {\bf{(B}} \cup {\bf{C)}}\)
e. \({{\bf{A}}^{\bf{c}}} \cap {{\bf{B}}^{\bf{c}}} \cap {{\bf{C}}^{\bf{c}}}\)
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:
\(\begin{aligned}{l}{\bf{a}}{\bf{.}}\;{{\bf{A}}^{\bf{c}}}\\{\bf{b}}{\bf{.}}\;{\bf{A}} \cup {\bf{B}}\\{\bf{c}}{\bf{.}}\;{\bf{B}} \cap {{\bf{C}}^{\bf{c}}}\\{\bf{d}}{\bf{.}}\;{{\bf{A}}^{\bf{c}}} \cap {{\bf{B}}^{\bf{c}}} \cap {{\bf{C}}^{\bf{c}}}\\{\bf{e}}{\bf{.}}\;\left( {{\bf{A}} \cup {\bf{B}}} \right) \cap {\bf{C}}\end{aligned}\)
Suppose that\(A \subset B\). Show that\({B^c} \subset {A^c}\).
Suppose that X has the standard normal distribution, and the conditional distribution of Y given X is the normal distribution with mean 2X 鈭� 3 and variance 12. Determine the marginal distribution of Y and the value of 蟻(X, Y ).
A box contains 24 light bulbs, of which four are defective. If a person selects four bulbs from the box at random, without replacement, what is the probability that all four bulbs will be defective?
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