probability

An absent-minded nurse is to give Mr. Brown a pill each day. The probability that the nurse forgets to administer the pill is 2/3. If he receives the pill, the probability that Mr. Brown will die is 1/3. If he does not get his pill, the probability that he will die is 3/4. Mr. Brown dies. What is the probability that the nurse forgot to give him his pill?

Linear problem using Microsoft Excel solver

Trying to solve problem using Excel Solver

C(n,r)=

Consider the recursive relationship for combinations: C(n,r) = C(n-1,r) + C(n-1,r-1) Prove this relationship algebraically using the mathematical definition of a combination, as well as that of the factorial function. Provide a logical explanation for this relationship (consider n objects as consisting of n-1 existing objects plus a new nth object. Given the ultimate goal of selecting r objects from the entire set of n, you must select objects from the set of n-1 objects and decide how the new nth object should join the existing selected sets.)

Probability

A set D is a subset of set C provided that a. every element of C is an element of D b. every element of D is an element of C c. at least one element of C is not an element of D d. at least one element of D is not an element C e. none of the above

Sets , subsets, element of a set, universal, and empty sets(Probability)

Events E and F are mutually exclusive and Pr(F) is not equal to 0. Which of the following must be true? a. E and F are independent b. Pr (E | F) = Pr(E) c. Pr(E "intersection symbol" F) = Pr(E) x Pr(F) d. Pr (E "union symbol" F)= Pr(E) + Pr(F) e. none of the above