Section 5.3 Homework

1.  Fill in each blank with the appropriate word or phrase.
The General Multiplication Rule states that P (A and B) = _________.

2.  Let A and B be events with P (A) = 0.5, P (B) = 0.8, and P (B|A) = 0.4.  Find P ( A and B).

3.  GED: In a certain high school, the probability that a student drops out is 0.05, and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.21. What is the probability that a randomly selected student gets a GED? Round your answer to four decimal places, if necessary.

The probability that the randomly selected student gets a GED is ______.

4.  Fill in each blank with the appropriate word or phrase.
Two events are ________ if the occurrence of one does not affect the probability that the other event occurs.

5.  Assume that a student is chosen at random from a class. Determine whether the events  A and  B are independent, mutually exclusive, or neither.

A: The student is a sophomore.
B: The student is a senior.

1. The events  A and  B are independent.
2. The events  A and  B are mutually exclusive.
3. The events  A and  B are neither independent nor mutually exclusive.

6.  Let A and B  be events with P (A) = 0.04, P (B) = 0.03 and P (A or B) = 0.07.

(a) Compute P (A and B) .

(b) Are A and B mutually exclusive? Explain.

(c) Are A  and B independent? Explain.

7. Genetics: A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of  individuals is categorized as follows. Write your answer as a fraction or a decimal, rounded to four decimal places.

(a) What is the probability that in a randomly sampled individual, gene 1  is recessive?
(b) What is the probability that in a randomly sampled individual, gene 2 is recessive?

(c) Given that gene  is recessive, what is the probability that gene 2 is recessive?

(d) Two genes are said to be in linkage equilibrium if the event that gene 1 is recessive is independent of the event that gene 2 is recessive. Are these genes in linkage equilibrium?

The probability that gene 1  is recessive in a randomly sampled individual is .

The probability that gene 2 is recessive in a randomly sampled individual is .

The probability that gene 2  is recessive given that gene 1  is recessive is .

The event that gene 1  is recessive ______  independent of the event that gene 2 is recessive.

The genes  _____ in linkage equilibrium.