How Do You Calculate the Probability of Both Events Occurring?

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SUMMARY

The probability of both Mr. Jones and Mr. Smith being selected for jury duty can be calculated using the provided probabilities: P(A) = 0.7 for Mr. Jones and P(B) = 0.4 for Mr. Smith, with the probability that neither is selected being P(A^{c} ∩ B^{c}) = 0.1. Applying the "and" rule, the formula P(A ∩ B) = P(A) + P(B) - P(A ∪ B) leads to the conclusion that P(A ∩ B) = 0.7 + 0.4 - (1 - 0.1) = 0.1. Thus, the probability that both are selected is 0.1.

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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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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
 

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