Pre-Algebra: Chapter 10-9
Probability of Independent and Dependent Events
There are 2 kinds of probability, independent and dependent events.
With independent events, like taking marbles out of a bag (but putting them back in – that is the number of marbles stay the same), the probability of 2 independent events can be found by multiplying the probability of the first event by the probability of the second event. The P(A and B) = P(A) * P(B)
With dependent events, (marbles taken out of a bag AND NOT returned – that is the numbers decrease in the bag), the probability of both events occuring is the product of the probability of A and the probability of B AFTER A occurs. P(A and B) = P(A) * P(B following A).
Algebra: Chapter 11-3
Simplifying Radical Expressions
sqrt(x^2) = square root (x^2) = x
Its easy to simplify radicals. You can break up numbers and variables, because multiplication is commutative. If asked to find the sqrt (square root) of 100, we could break up 100 into 25 * 4. We know that the sqrt (square root) of 25 = 5 and the sqrt of 4 = 2, then the sqrt of 100 is 5 * 2 = 10. You can do the same with variables that have exponents.
If asked to find the sqrt of a variable with even exponents, sqrt(x^6) for example, the answer is just the variable with the exponent divided in 2. So for sqrt(x^6), the answer is (x^3). If the variable has odd exponents, like (x^27), convert that to (x^26)*(x^1) and then take the sqrt of (x^26) * sqrt(x^1) = (x^13)* sqrt(x).