$A\cup B$ can be expressed as the union of two mutual exclusive events in the following way:

$A\cup B=A\cup (B-AB)$

Express $A\cup B\cup C$ in a similar way.

$A\cup B=A\cup (B-AB)$

Express $A\cup B\cup C$ in a similar way.

Lorena Lester
2022-07-20
Answered

$A\cup B$ can be expressed as the union of two mutual exclusive events in the following way:

$A\cup B=A\cup (B-AB)$

Express $A\cup B\cup C$ in a similar way.

$A\cup B=A\cup (B-AB)$

Express $A\cup B\cup C$ in a similar way.

You can still ask an expert for help

escobamesmo

Answered 2022-07-21
Author has **18** answers

$A\cup B\cup C=A\cup ({A}^{c}\cap B)\cup ({A}^{c}\cap {B}^{c}\cap C).$

The intuition is as follows. The first term (namely $A$), gets us all the elements of $A$. The second term (namely ${A}^{c}\cap B$) gets us all the elements in $B$, but leaves out those that we already got with our first term. Etc.

The intuition is as follows. The first term (namely $A$), gets us all the elements of $A$. The second term (namely ${A}^{c}\cap B$) gets us all the elements in $B$, but leaves out those that we already got with our first term. Etc.

asked 2021-09-08

John charges his cell phone only when it is fully drained. The length of time, in hours, between charges of his cell phone is normally distributed with mean 31 and variance 64.

Probability(Cell phone will last between 40.52 and 42.92 hours)

Probability(Cell phone will last between 40.52 and 42.92 hours)

asked 2021-11-21

An automobile manufacturer produces a certain model of car. The fuel economy figures of these cars are normally distributed with a mean mileage per gallon (mpg) of 36.8 and a standard deviation of 1.3

(a) What is the probability that one of these cars will have an mpg of more than 37.5?

(b) What is the probability that one of these cars will have an mpg of less than 35?

(c) What is the probability that one of these cars will have an mpg of less than 40?

(a) What is the probability that one of these cars will have an mpg of more than 37.5?

(b) What is the probability that one of these cars will have an mpg of less than 35?

(c) What is the probability that one of these cars will have an mpg of less than 40?

asked 2021-01-13

Convert the binomial probability to a normal distribution probability using continuity correction.

asked 2021-12-06

Consider a Poisson distribution with a mean of two occurrences per time period.

Write the appropriate Poisson probability function to determine the probability of x occurrences in three time periods.

Write the appropriate Poisson probability function to determine the probability of x occurrences in three time periods.

asked 2021-09-15

The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of eight syringes taken from the batch. Suppose the batch contains 1% defective syringes.

Find ? (in terms of the number of syringes).

What is the expected number of defective syringes the inspector will find?

What is the probability that the batch will be accepted?

Find ? (in terms of the number of syringes)

Find ? (in terms of the number of syringes).

What is the expected number of defective syringes the inspector will find?

What is the probability that the batch will be accepted?

Find ? (in terms of the number of syringes)

asked 2021-10-25

A fair quarter is flipped 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 distribution table. (Enter your answers to three decimal places.)
Find the probability of getting exactly three tails.
(d) Find the probability of getting exactly three tails.
(d) Find the probability of getting exactly three tails.

asked 2021-12-12

Complete the table and construct the probability histogram for a binomial random variable x with $n=6\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}p=0.5$ .

$$\begin{array}{|cccccccc|}\hline x& 0& 1& 2& 3& 4& 5& 6\\ p(x)\\ \hline\end{array}$$