Question

Suppose that A and B are independent events such that P(A)=0.10 and P(\bar{B})=0.20 Find P(A\cap B) and P(A\cup B)

Ratios, rates, proportions
ANSWERED
asked 2021-05-07
Suppose that A and B are independent events such that \(P(A)=0.10\) and \(P(\bar{B})=0.20\)
Find \(P(A\cap B)\) and \(P(A\cup B)\)

Answers (1)

2021-05-08
Step 1
The value of \(P(A\cap B)\) is obtained below:
From the given information, the events A and B are independent events and the probability values are
\(P(A)=0.10\), and the value of \(P(B)\) is,
\(P(B)=1-P(\bar{B})\)
\(=(1-0.20)\)
\(P(B)=0.80\)
The required probability is,
\(P(A\cap B)=P(A)\times P(B)\)
\(=0.10\times0.80\)
\(=0.08\)
The value of \(P(A\cap B)\) is \(0.08\)
The value of \(P(A\cap B)\) is obtained by taking the product of probability of event A and the probability of event B. It can be expected that \(2\%\) of the event A and B occurs.
Step 2
The value of \(P(A\cup B)\) is obtained as shown below:
The probability is,
\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
\(=0.10+0.80-0.08\)
\(=0.90-0.08\)
\(=0.82\)
The value of \(P(A\cup B)\) is \(0.82\).
The value of \(P(A\cup B)\) is obtained by adding the individual probabilities and then subtracting the probability of A and B to the resulted value. It can be expected that about \(82\%\) of times event A or B happens.
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-05-14
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)
a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)
MPa
State which estimator you used.
\(x\)
\(p?\)
\(\frac{s}{x}\)
\(s\)
\(\tilde{\chi}\)
b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).
MPa
State which estimator you used.
\(s\)
\(x\)
\(p?\)
\(\tilde{\chi}\)
\(\frac{s}{x}\)
c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)
MPa
Interpret this point estimate.
This estimate describes the linearity of the data.
This estimate describes the bias of the data.
This estimate describes the spread of the data.
This estimate describes the center of the data.
Which estimator did you use?
\(\tilde{\chi}\)
\(x\)
\(s\)
\(\frac{s}{x}\)
\(p?\)
d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)
e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)
State which estimator you used.
\(p?\)
\(\tilde{\chi}\)
\(s\)
\(\frac{s}{x}\)
\(x\)
asked 2021-06-18
How many rational numbers are there between -10 and 10? Explain.
asked 2021-06-18
tempco corporation has a machine that produces 18 3/4 baseball gloves each hour. in the last 2days. the machines has run for a total of 20 hours. how many baseball gloves has tempco produced?
asked 2021-06-11
For some positive value of z, the probability that a standard normal variable is between 0 and Z is .3770. Which is the value of z?
...