Chapter 13 – Probability

1. Define conditional probability.

2. State the multiplication theorem of probability.

3. What is P(A|B) when A and B are independent?

4. State Bayes' theorem.

5. What is the range of a probability?

6. If A and B are mutually exclusive, can they be independent when both have positive probability?

1. If P(A)=1/2 and P(B)=1/3 and A,B are independent, find P(A∩B).

2. A box contains 3 red and 2 blue balls. Find the probability of drawing a red ball.

3. Two events have probabilities 1/2 and 1/3 and are mutually exclusive. Find P(A∪B).

1. Two cards are drawn successively without replacement from a pack. Find the probability that both are aces.

2. Three machines produce items with different defect rates. Formulate how Bayes' theorem can be used to find the probability that a defective item came from a specified machine.

3. If P(A)=0.6, P(B)=0.5 and P(A∩B)=0.3, determine whether A and B are independent.

1. Three boxes contain different proportions of red and blue balls. A box is selected at random and a red ball is drawn. Using Bayes' theorem, derive the probability that the selected ball came from each box. Explain why the prior probabilities must be included.