Probability Examples and Explanations

The National Vaccine Information Center estimates that 90% of Americans have had chickenpox by the time they reach adulthood.
What is the probability that exactly 3 out of a new sample of 100 American adults have not had chickenpox in their childhood?

a simple binary communication channel carries messages by using only two signals, say 0 and 1. We assume that, for a given binary channel, 40% of the time a | is transmitted; the probability that a transmitted 0 is correctly received is 0.90 and the probability that a transmitted | is correctly received is 0.95. the probability of a 1 being received

A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute the probability of a value between 55.0 and 70.0.

The National Vaccine Information Center estimates that 90% of Americans have had chickenpox by the time they reach adulthood.
Suppose we take a random sample of 100 American adults. Is the use of the binomial distribution appropriate for calculating the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood? Explain.

The probability that an automobile being filled with gasoline will also need an oil change is 0.35; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and filter need changing is 0.25.
If a new oil filter is needed, what is the probability that the oil has to be changed ?

A tar quarters fipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in the binomial probability cistribution table. (Enter your answers to three decimal places}
(a)Find the probebilty of getting exactly three heads.
(b) Find the probabilty of getting exactly two heads.
(c) Find the probabilty of getting two or more heads.
(d) Find the probability of getting exactiy three tails.

The National Vaccine Information Center estimates that 90% of Americans have had chickenpox by the time they reach adulthood.
Calculate the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood.

Probability of a author writing a good book is ${\displaystyle \frac{1}{2}}$
The probability of the author publishing a good book is ${\displaystyle \frac{2}{3}}$
The probability of the author publishing NOT a good book is ${\displaystyle \frac{1}{4}}$
If the author writes two books, then find the probability that at-least one book being published.

Sue and Ann are taking the same English class but they do not study together, so whether one passes will be Independent of whether the other passes. In other words, “Sue passes and “Ann passes” are assumed to be independent events. The probebiity that Sue passes English is 0.8 and the probablity that Ann passes English is 0.75 If Ann passes, what then is the conditional probability that Sue also passes?

An oil company is bidding for the rights to drill a well in field A and awell in field B. The probability it will drill a well in field A is 40%. Ifit does, the probability the well will be successful is 45%, The probability it will drill a well in field B is 30% Ifit

An oil company is bidding for the rights to drill a well in field A and awell in field B. The probability it will drill a well in field A is 40%. Ifit does, the probability the well will be successful is 45%, The probability it will drill a well in field B is 30% Ifit

A company makes a profit each month with probability 0.7. What is the probability that it makes a profit in exactly two of the next three months?
Conditional probability: Yes or No

Intrusion detection systems.
A computer intrusion detection system (IDS) is designed to provide an alarm whenever an intrusion (e.g., unauthorized access) is being attempted into a computer system.
A probabilistic evaluation of a system with two independently operating intrusion detection systems (a double IDS) was published in the Journal of Research of the National Institute of Standards and Technology (Nov.–Dec. 2003).
Consider a double IDS with system A and system B. If there is an intruder, system A sounds an alarm with probability .9 and system B sounds an alarm with probability .95.
If there is no intruder, the probability that system A sounds an alarm (i.e., a false alarm) is .2 and the probability that system B sounds an alarm is .1.
If there is no intruder, what is the probability that both systems sound an alarm?

What is the probability that a fair die never comes up an even number when it is rolled six times?

a simple binary communication channel carries messages by using only two signals, say 0 and 1. We assume that, for a given binary channel, 40% of the time a | is transmitted; the probability that a transmitted 0 is correctly received is 0.90 and the probability that a transmitted | is correctly received is 0.95. given a | is received, the probability that 1 was transmitted.

The probability that an automobile being filled with gasoline will also need an oil change is 0.37; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and filter need changing is 0.20.
If a new oil filter is needed, what is the probability that the oil has to be changed?

Suppose we are testing ${\displaystyle H_0:p=.20}$ vs ${\displaystyle H_a:p>>.20}$ and TS=2.34. What is the p-value?