How Do You Calculate the Probability of Both Events Occurring?

In summary, the probability of both Mr. Jones and Mr. Smith being selected for jury duty is 30%. This can be found by using the "and" rule and the given probabilities: P(A) = 0.7, P(B) = 0.4, P(A^{c}\capB^{c}) = 0.1. By rearranging the equation P(A^{c}\capB^{c}) + P(A\cupB) = 1, we can find P(A\capB).
  • #1
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Homework Statement



The probability of Mr. Jones being selected for jury duty is 70%. The probability that Mr. Smith will be selected is 40%. The probability that neither will be selected is 10%. What is the probability that both are selected?

Homework Equations



the "and" rule

The Attempt at a Solution



(.4) + (.7) - (.1) = 1
 
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  • #2
first of all i think you should get a good book on probability since most of the problems posted by you are quite basic and you seem to be guessing the answers..

in this question

given is

P(A) = 0.7
P(B) = 0.4
P(A[itex]^{c}[/itex][itex]\cap[/itex]B[itex]^{c}[/itex])= 0.1

you have to find P(A[itex]\cap[/itex]B)

use

P(A[itex]^{c}[/itex][itex]\cap[/itex]B[itex]^{c}[/itex]) + P(A[itex]\cup[/itex]B) =1
 

FAQ: How Do You Calculate the Probability of Both Events Occurring?

What is the difference between statistics and probability?

Statistics is the study of collecting, analyzing, and interpreting data, while probability is the study of the likelihood of an event occurring based on the available data.

How are statistics and probability used in real life?

Statistics and probability are used in a variety of fields, such as business, finance, medicine, and social sciences. They are used to make informed decisions, make predictions, and identify patterns and trends in data.

What are some common misconceptions about statistics and probability?

One common misconception is that statistics and probability can predict the future with 100% accuracy. In reality, they can only provide a likelihood or probability of an event occurring based on available data. Another misconception is that correlation implies causation, when in fact, correlation does not necessarily mean causation.

How can I improve my understanding of statistics and probability?

Some ways to improve your understanding of statistics and probability include practicing with real-life examples, working with data sets, and seeking out additional resources such as textbooks, online courses, or tutoring.

What are some common applications of statistics and probability in research?

Statistics and probability are used in research to analyze and interpret data, test hypotheses, and make predictions. They are also used to determine sample sizes, design experiments, and assess the reliability and validity of results.

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