For two events a and b show that p (a∩b) ≥ p (a)+p (b)−1.

(hint: apply de morgan’s law and then the bonferroni inequality).

derive below results 1 to 4 from axioms 1 to 3 given in section 2.1.2 in the textbook.

result 1: p (ac) = 1 − p(a)

result 2 : for any two events a and b, p (a∪b) = p (a)+p (b)−p (a∩b)

result 3: for any two events a and b, p(a) = p(a ∩ b) + p (a ∩ bc)

result 4: if b ⊂ a, thena∩b = b. therefore p (a)−p (b) = p (a ∩ bc) and p (a) p(b).

You work for a lender that requires a 20% down payment and uses the standard depth to income ratio to determine a person‘s a little eligibility for a home loan of the following choose the person that you would rate the highest on their eligibility for a home loan

The length of the largest fish is 967.74 times greater than the length of the smallest fish. select a variable expression that shows the length of the largest fish, if 8 is the length of the smallest fish. a. s + 967.74 b. \[ \frac{967.74}{s} \] c. 967.74 - s d. 967. 74s

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function.how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions