SOLUTION: Suppose an experiment has only two outcomes, e1 and e2, where p(e1)= p and p(e2)= p^2. What is p?

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Question 706469: Suppose an experiment has only two outcomes, e1 and e2, where p(e1)= p and p(e2)= p^2. What is p?
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

clearly in this space p%5E2%2Bp=1.... you solve for p

p%5E2%2Bp-1=0....use quadratic formula

p=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ...note that a=1, b=1 and c=-1

p=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+

p=+%28-1+%2B-+sqrt%28+1%2B4+%29%29%2F2+

p=+%28-1+%2B-+sqrt%28+5+%29%29%2F2+

p=+%28-1+%2B-2.24%29%2F2+
solution:

p=+%28-1+%2B2.24%29%2F2+
p=+%281.24%29%2F2+
p=+0.62+

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose an experiment has only two outcomes, e1 and e2, where p(e1)= p and p(e2)= p^2. What is p?
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Equation:
p + p^2 = 1
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p^2 + p -1 = 0
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Quadratic Formula:
p = [-1 +- sqrt(1-4*1*-1)]/2
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To get a positive answer:
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p = [-1 +sqrt(5)]/2
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p = 0.6180
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cheers,
Stan H.
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