In a certain region of the country it is known from past experience that the probability of selecting an adult over 40 years of
1 answer:
Answer: Our required probability is 0.406.
Step-by-step explanation:
Since we have given that
Probability of selecting an adult over 40 years of age with cancer = 0.05
Probability of a doctor correctly diagnosing a person with cancer as having the disease = 0.78
Probability of incorrectly diagnosing a person without cancer as having the disease = 0.06
Let A be the given event i.e. adult over 40 years of age with cancer. P(A) = 0.05.
So, P(A')=1-0.05 = 0.95
Let C be the event that having cancer.
P(C|A)=0.78
P(C|A')=0.06
So, using the Bayes theorem, we get that
Hence, our required probability is 0.406.
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Answer:
Given: In triangle ABC and triangle DBE where DE is parallel to AC.
In ΔABC and ΔDBE
[Given]
As we know, a line that cuts across two or more parallel lines. In the given figure, the line AB is a transversal.
Line segment AB is transversal that intersects two parallel lines. [Conclusion from statement 1.]
Corresponding angles theorem: two parallel lines are cut by a transversal, then the corresponding angles are congruent.
then;
and
Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.
by Reflexive property of equality:
By AAA (Angle Angle Angle) similarity postulates states that all three pairs of corresponding angles are the same then, the triangles are similar
therefore, by AAA similarity postulates theorem
Similar triangles are triangles with equal corresponding angles and proportionate side.
then, we have;
[By definition of similar triangles]
therefore, the missing statement and the reasons are
Statement Reason
3. Corresponding angles theorem
and
5. AAA similarity postulates
6. BD over BA Definition of similar triangle