BUSI 230 HW 5.3 Conditional Probability and the Multiplication Rule Assignment solutions answers

BUSI 230 HW 5.3 Conditional Probability and the Multiplication Rule Assignment solutions complete answers 

 

Just put your values given and automatically provide answers for you!

 

Fill in each blank with the appropriate word or phrase.

A probability that is computed with the knowledge of additional information is called .

 

The General Multiplication Rule states that .

 

Two events are  if the occurrence of one does not affect the probability that the other event occurs.

 

Let A and B be events with P(A)=0.2, P(B)=0.98, and P(B/A)=0.1. Find P(A and B).

 

Let A and B be events with P(A)=0.2, P(B)=0.7. Assume that A and B are independent. Find P(A and B).

 

A fair coin is tossed five times. What is the probability that the sequence of tosses is HTHTH? Write your answer as a fraction or a decimal, rounded to four decimal places.

The probability that the sequence of tosses is HTHT is

 

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 woman.

B: The student belongs to a sorority.

 

Let A and B be events with P(A)=0.3, P(B)=0.2, and P(A or B)=0.18.

(a) Are A and B independent? Explain.

(b) Compute P(A and B).

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

 

An unfair coin has probability 0.4 of landing heads. The coin is tossed seven times. What is the probability that it lands heads at least once? Round the answer to four decimal places.

P(Lands heads at least once)=

 

Shuffle: Charles has three songs on a playlist. Each song is by a different artist. The artists are Drake, Ed Sheeran, and BTS. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Ed Sheeran and the second song is by Drake? Write your answer as a fraction or a decimal, rounded to four decimal places.

The probability that the first song is by Ed Sheeran and the second song is by Drake is

 

Let's eat: A fast-food restaurant chain has 591 outlets in the United States. The following table categorizes them by city population size and location, and presents the number of restaurants in each category. A restaurant is to be chosen at random from the 591 to test market a new menu. Round your answers to four decimal places.

(a) Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the Northeast?

(b) Given that the restaurant is located in the Southeast, what is the probability that it is in a city with a population under 50,000?

(c) Given that the restaurant is located in the Southwest, what is the probability that it is in a city with a population of 500,000 or less?

(d) Given that the restaurant is located in a city with a population of 500,000 or less, what is the probability that it is in the Southwest?

(e) Given that the restaurant is located in the South (either SE or SW), what is the probability that it is in a city with a population of 50,000 or more?

 

Genetics: A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 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 1 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?

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

 

Stay in school: In a recent school year in the state of Washington, there were 324,000 high school students. Of these, 157,000 were girls and 167,000 were boys. Among the girls, 70,700 dropped out of school, and among the boys, 10,300 dropped out. A student is chosen at random. Round the answers to four decimal places.

(a) What is the probability that the student is male?

(b) What is the probability that the student dropped out?

(c) What is the probability that the student is male and dropped out?

(d) Given that the student is male, what is the probability that he dropped out?

(e) Given that the student dropped out, what is the probability that the student is male?

(a) What is the probability that the student is female?

 

GED: In a certain high school, the probability that a student drops out is 0.03, and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.31. 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

 

Defective components: A lot of 9 components contains 4 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Write your answer as a fraction or a decimal, rounded to four decimal places.

Are A dn B independent? Explain.

 

Lottery: Every day, Jorge buys a lottery ticket. Each ticket has a probability of 0.4 of winning a prize. After sex days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places.

The probability that Jorge has won at least one prize is