Find the indicated probability using the standard normal distribution. P(-2.72 < z < 2.72)
. Det IQ11 Suppose that P(AB) 04 (a) PAn B) (b) P(A'nB) and P(B) 0.5, Determine the following
p(a) = .59 p(b) = .30 p(anb) =.21 find p(a'ub') and find p(a'nb')
Prove that P(A' n B') = 1 + P(A n B)- P(A)- P(B)
Q = 19 - 1P + 2PS where P is the price of the product and Ps the price of a substitute good. The price of the substitute good is $2.00. Suppose P=$0.90 The price elasticity of demand is? Please walk me through the quantity calculation as well, I'm struggling to get the right answer. Thank you!
8. Suppose that B = {p € Q: p? > 2}. Prove that B contains no smallest element.
1. Use the formula P(A) PABP(B) + P(AlBc)P(B") to prove that if P(AB) P (AlBc) then A and B are independent. Then prove the converse (that if A and B are independent then P(AIB)- P(ABe). [Assume that P(B) > 0 and P(B) > 0.]
4. Prove that for any formulae A and B and variable p, A[p := B] is a well-formed!) formula.
1. Prove“inclusion-exclusion,”thatP(A∪B)=P(A)+P(B)−P(A∩B). 2. Prove the “unionbound, ”thatP(A1∪A2)≤P(A1)+P(A2). Under what conditions does the equality hold? 3. Provethat, for A1 andA2 disjoint, P(A1∪A2|B)=P(A1|B)+P(A2|B). 4. A and B are independent events with nonzero probability. Prove whether or not A and Bc are independent.
10/10 will rate. Thanks in advance! If A and B are mutually exclusive, P(A) 0.3, and P(B) 047, find (c) P(AU B); (e) P(AnB); () P(A'nB). (d) P(An B);