Mutually exclusive stats homework

  • Thread starter Thread starter daewoo
  • Start date Start date
  • Tags Tags
    Homework Stats
AI Thread Summary
To solve for P(B) given P(A) = 0.8 and P(A or B) = 0.9, two scenarios are considered: independence and mutual exclusivity. For independent events, the formula P(A or B) = P(A) + P(B) - P(A and B) applies, where P(A and B) can be calculated as P(A) x P(B). In the case of mutually exclusive events, P(A or B) simplifies to P(A) + P(B) since P(A and B) equals zero. The confusion arises in isolating P(B) in both scenarios, highlighting the need for clarity in applying the correct formulas. Understanding these concepts is crucial for accurately determining probabilities in statistics.
daewoo
Messages
25
Reaction score
0

Homework Statement


Suppose that P(A) = 0.8 and P(A or B) = 0.9 , determine P(B) If
a) A and B are independent
b) A and B are mutually exclusive


Homework Equations


for Independence P(A and B) = P(A) x P(B)
for Mutually Exclusive P(A or B) = P(A) + P(B)


The Attempt at a Solution


for A) just by the formula i can say that P(A and B) = P(A) x P(B)
but i don't see still how i can find P(B), the P(A or B) part is really confusing to me.
 
Physics news on Phys.org
For not mutually exclusive, part (A), p(A or B)= P(A)+ P(B)- P(A and B). Put the values into both that AND P(A and B)= P(A)xP(B).
 
hm thanks, but how do you find out what P(B) alone is because i can't use that formula anyways.
 
You can't use WHAT formula? And why not?
 
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
Back
Top