Answer:
A and B are not independent events because P(A|B)≠P(A)
is the correct answer.
Step-by-step explanation:
If A and B are independent then we must have
P(AB) = P(A) P(B) and also
P(A/B) = P(A)
We are given that
A and B are two events.
Let P(A)=0.5 , P(B)=0.25 , and P(A and B)=0.15 .
P(A/B) = P(AB)/P(B) = 0.15/0.5 = 0.3
i.e. P(A/B) is not equal P(A)
Similarly P(B/A) = P(AB)/P(A) = 0.15/0.25 = 0.6 not equal to P(B)
Hence A and B are not independent.
Answer:
(5, -5)
General Formulas and Concepts:
<u>Pre-Algebra
</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- <u>
</u>Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Coordinates (x, y)
- Terms/Coefficients
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
2x - 3y = 25
5x + 3y = 10
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Elimination</em>
- Combine two equations: 7x = 35
- [Division Property of Equality] Divide 7 on both sides: x = 5
<u>Step 3: Solve for </u><em><u>y</u></em>
- Substitute in <em>x</em> [1st Equation]: 2(5) - 3y = 25
- Multiply: 10 - 3y = 25
- [Subtraction Property of Equality] Subtract 10 on both sides: -3y = 15
- [Division Property of Equality] Divide -3 on both sides: y = -5
