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CALCULUS AND ANALYSIS
PRECALCULUS
PROBABILITY AND COMBINATORICS
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Calculus and Analysis
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Transformations of functions
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Probability and combinatorics Answers
Probability and combinatorics
asked 2021-02-25
Can two events with nonzero probabilities be both independent and mutually exclusive? Explain your reasoning.
Probability and combinatorics
asked 2021-02-21
If Jeremy has 4 times as many dimes as nickels and they have a combined value of 360 cents, how many of each coin does he have?
Probability and combinatorics
asked 2021-02-12
Let the sequence of events E1, E2, . . . , En be independent, and assume that
\(\displaystyle{P}{\left({E}{i}\right)}=\frac{{1}}{{{i}+{1}}}\)
. Show that
\(\displaystyle{P}{\left({E}{1}∪···∪{E}{n}\right)}=\frac{{n}}{{{n}+{1}}}\)
Probability and combinatorics
asked 2021-02-05
A radio station gives a pair of concert tickets to the 6th called who knows the birthday of the performer. For each person who calls, the probability is.75 of knowing the performer birthday. All calls are independent.
a. What is the PMF (Probability Mass Function) of L, the number of calls necessary to find the winner?
b. What is the probability of finding the winner on the 10th call?
c. What is the probability that the station will need 9 or more calls to find a winner?
Probability and combinatorics
asked 2021-01-31
In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50, both averaged 12 years of schooling completed, with an SD of 3 years.
a) Predict the educational level of a woman whose husband has completed 18 years of schooling b) Predict the educational level of a man whose wife has completed 15 years of schooling. c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible?
Probability and combinatorics
asked 2021-01-19
Suppose that a batch of 100 items contains 6 that are defective and 94 that are non-defective. If X is the number of defective items in a randomly drawn sample of 10 items, find (a)P{X = 0} and (b) P {X > 2}.
Probability and combinatorics
asked 2021-01-19
Suppose the alphabet consists of just {a,b,c,d,e}. Consider strings of letters that show repetitions. How many 4-letter strings are there that do not contain “aa"?
Probability and combinatorics
asked 2021-01-10
The problem reads: Suppose
\(\displaystyle{P}{\left({X}_{{1}}\right)}={.75}\)
and
\(\displaystyle{P}{\left({Y}_{{2}}{\mid}{X}_{{1}}\right)}={.40}\)
. What is the joint probability of
\(\displaystyle{X}_{{1}}\)
and
\(\displaystyle{Y}_{{2}}\)
?
This is how I answered it. P(
\(\displaystyle{X}_{{1}}\)
and
\(\displaystyle{Y}_{{2}}\)
)
\(\displaystyle={P}{\left({X}_{{1}}\right)}\times{P}{\left({Y}_{{1}}{\mid}{X}_{{1}}\right)}={.75}\times{.40}={0.3}.\)
What I don't understand is how do you get the
\(\displaystyle{P}{\left({Y}_{{1}}{\mid}{X}_{{1}}\right)}\)
? I am totally new to Statistices and I need to understand each part of the process in order to get the whole concept. Can anyone help me to understand why the P and X exist and what they represent?
Probability and combinatorics
asked 2021-01-10
Prove that for
\({n}\ge{2},{2}\cdot{\left(\begin{matrix}{n}\\{2}\end{matrix}\right)}+{\left(\begin{matrix}{n}\\{1}\end{matrix}\right)}={n}^{2}\)
Probability and combinatorics
asked 2021-01-08
Given the following: P(A) = 0.3 P(B) = 0.2 P(A or B) = 0.5 P(A and B) = 0
Which of the following is true?
A and B are disjoint.
A and B are neither disjoint nor independent.
A and B are independent.
A and B are disjoint and independent.
Probability and combinatorics
asked 2021-01-04
Suppose a class consists of 5 students majoring in Computer Science, 5 students majoring in Chemistry and 3 students majoring in Mathematics. How many ways are possible to form a group of 3 students if each group should consist at most 2 students majoring in Computer Science?
Probability and combinatorics
asked 2021-01-04
Let D be the set of all students at your school, and let M(s) be a ”s is a math major”, let C(s)”s is a computer science student”, and let E(s) be ”s is an engineering student.” Express each of the following statements using quantifiers, variables, and predicates M(s), C(s) and E(s)
Probability and combinatorics
asked 2021-01-02
Prove that
\(\displaystyle\sum_{j=1}^{n} 2^{j}=2^{n+1}-2\)
\(\forall\geq1\)
Probability and combinatorics
asked 2020-12-30
To combine like terms, ___ their coefficients and ___ the same variables and exponents.
Probability and combinatorics
asked 2020-12-25
Let the sample space be
\(S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.\)
Suppose the outcomes are equally likely. Compute the probability of the event E="an even number less than 9."
Probability and combinatorics
asked 2020-12-24
Suppose a class consists of 4 students majoring in Mathematics, 3 students majoring in Chemistry and 4 students majoring in Computer Science. How many compositions are possible to form a group of 3 students if each group should consist at most 2 students majoring in Computer Science?
Probability and combinatorics
asked 2020-12-22
A bag contains 2 red checkers and 6 black checkers. A checker is selected, kept out of the bag, and then another checker is selected. What is P(black, then red)?
Probability and combinatorics
asked 2020-12-17
9 students are in a math class. How many different ways can you choose 6 people for a group?
Probability and combinatorics
asked 2020-12-17
Dree rolls a strike in 6 out of the 10 frames of bowling. What is the experimental probability that Dree will roll a strike in the first frame of the next game? Explain why a number cube would not be a good way to simulate this situation.
Probability and combinatorics
asked 2020-12-13
A radio station gives a pair of concert tickets to the six caller who knows the birthday of the performer. For each person who calls, the probability is 0.75 of knowing the performer's birthday. All calls are independent.
a) What is the PMF of L, the numberof calls necessary to find the winner? MSK b) What is the probability of finding the winner on the tenth caller?
c) What is the probability of finding the winner on the tenth caller?
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