A shipment box contains 12 graphing calculators, out of which 2 are defective. A calculator is drawn at random from the box and then, without replacement, a second calculator is drawn. Discuss whether the equally likely assumption would be appropriate for the sample space S = G G , G D , D G , D D where G is a good calculator and D is a defective one.
A shipment box contains 12 graphing calculators, out of which 2 are defective. A calculator is drawn at random from the box and then, without replacement, a second calculator is drawn. Discuss whether the equally likely assumption would be appropriate for the sample space S = G G , G D , D G , D D where G is a good calculator and D is a defective one.
A shipment box contains
12
graphing calculators, out of which
2
are defective. A calculator is drawn at random from the box and then, without replacement, a second calculator is drawn. Discuss whether the equally likely assumption would be appropriate for the sample space
S
=
G
G
,
G
D
,
D
G
,
D
D
where
G
is a good calculator and
D
is a defective one.
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
4.
5.
6.
Prove that p (gp) is a tautology using the laws of propositional logic.
Prove that p((pVq) → q) is a tautology using the laws of propositional logic.
Let us say a natural number n is ok if there are two natural numbers whose sum
is n and whose product is n. (Convention: the natural numbers consist of 0, 1, 2,...)
(a) Give a logical expression that means "n is ok".
(b) Show that 0 and 4 are both ok.
(c) Give a logical expression that means "every natural number is ok".
(d) Give a logical expression that means "it is not the case that every number is ok". Push
the negations into the expression as far as possible.
7.
Let E(x, y) be a two-variable predicate meaning "x likes to eat y", where the
domain of x is people and the domain of y is foods. Write logical expressions that represent
the following English propositions:
(a) Alice doesn't like to eat pizza.
(b) Everybody likes to eat at least one food.
(c) Every student likes to eat at least one food other than pizza.
(d) Everyone other than Alice likes to eat at least two different foods.
(e) There are two different people that like to eat the same food.
Chapter 8 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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