Math - Probability

Let A be an event within the sample spaceS, and letn(A)=a andn(S)=s. Evaluate and simplify

P(A)+P(A').

A bag contains fifty blue and fifty green marbles. Two marbles at a time are randomly selected. If both aregreen, they are placed in boxA; if both areblue, in boxB; if one is green and the other isblue, in box C. After all marbles aredrawn, what is the probability that the number of marbles in box A and box B are thesame?

Let A be an event within the sample spaceS, and letn(A)=a andn(S)=s.

Use the theoretical probability formula to expressP(A) andPA.

Let A be an event within the sample spaceS, and letn(A)=a andn(S)=s. Use the complements principle of counting to find an expression forn(A).

Suppose, for a givenexperiment, A,B, C, and D areevents, all mutually exclusive of oneanother, such thatABCD=S (the samplespace). By extending the addition rule ofprobability, thatis, if A and B are mutuallyexclusive, thenP(A orB)=P(A)+P(B) to thiscase, and utilizing the probability property that the probability of a certain event is1, what statement can youmake?

Let x denote the sum of two distinct numbers selected randomly from the set of numbers

{1,2,3,4,5}.

Construct the probability distribution for the random variable x.

Amanda has4 office assistants. If A is the event that at least3 of them are men and B is the event that at least3 of them arewomen, are A and B mutuallyexclusive?

If a number is chosen randomly from the set of numbers{1, 2,3, 4,...,

16}, find the probability of getting acomposite number.

For the experiment of drawing a single card from a standard52-card deck, find (a) theprobability, and (b) the odds infavor, that you do not drawaqueen.

For the experiment of rolling a single fairdie, find the probability that the number rolled is odd or even.

For the experiment of rolling a single fairdie, find the probability of obtaining notlessthan4.

Give the correct numerical response. If A and B areevents, with P(A)= 1/5

and P(B)=2/3, andP(A and B)=1/3, thenP(A orB) is___.

Assuming that boy and girl babies are equallylikely, what would beKathy's probability of having

atmostone daughter if she were to have four childrenaltogether? (You may want to use a tree diagram to construct the samplespace.)