SOLUTION: It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey

Question 1200232: It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. What is the probability that we must survey just one or two California residents until we find a California resident who does not have adequate earthquake supplies? (three decimal places)
Answer by ikleyn(52810) (Show Source): You can put this solution on YOUR website!
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It has been estimated that only about 30% of California residents have adequate earthquake supplies.
Suppose we are interested in the number of California residents we must survey
until we find a resident who does not have adequate earthquake supplies.
What is the probability that we must survey just one or two California residents
until we find a California resident who does not have adequate earthquake supplies?
(three decimal places)
~~~~~~~~~~~~~~~~~~~

We have an experiment which produces success (Yes) in 30% cases;
it produces failure (No) in the rest 70% cases.


They want you calculate probability of getting sequences (Yes,No)  or (Yes,Yes,No) 

and then calculate the mathematical expectation

    E = 1*P(Yes,No) + 2*P(Yes,Yes,No).   <<<---===  factor 2 in the second addend represents two "Yes".


This mathematical expectation will give you the answer on  " the number of California residents 
we must survey until we find a resident who does not have adequate earthquake supplies "
under given restrictions. 



It is easy to compute the probabilities

    P(Yes,No) = 0.3*0.7 = 0.21;  P(Yes,Yes,No) = 0.3*0.3*0.7 = 0.063.



Thus the  mathematical expectation to the problem's question is

    E = 1*P(Yes,No) + 2*P(Yes,Yes,No) = 1*(0.3*0.7) + 2*(0.3*0.3*0.7) = 0.21 + 2*0.063 = 0.336.    


The    to the problem question is this value of the mathematical expectation  E= 0.336.

Solved.

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