I need assistance with a few questions,

1.) Part 1?

Let A and B be events with P(A) = 0.8, P(B) = 0.2, and P(A and B) = 0.18. (a) Are A and B independent? Explain. (b) Compute P (A or B). (c) Are A and B mutually exclusive? Explain. Part: 0 / 3 Part 1 of 3 (a) Are A and B independent? Explain. The events A and B are independent since (Choose one)ent since (Choose one) P(A) . P(B) =P A and B P(A) . P(B) + P(A and B P(A and B) P (A and B =\fShuffle: Charles has six songs on a playlist. Each song is by a different artist. The artists are Shakira, Madonna, Adam Rickitt, Evan & Jaron, Stephen Gately, and Stevie Wonder. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Madonna and the second song is by Adam Rickitt? Write your answer as a fraction or a decimal, rounded to four decimal places. The probability that the first song is by Madonna and the second song is by Adam Rickitt isLet's eat: A fastfood restaurant chain has 586 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 586 to test market a new menu. Round your answers to four decimal places. Population Region or '3\"? N E SE 5w mw Under 50,000 25 33 13 3 50,000 500,000 60 E7 71 30 Over 500,000 146 23 27 63 (Send data in Excel a} (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 lessr 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? Part 1 of 5 Given that the restaurant is located in a city with a population over 500,000r the probability that it is in the Northeast is D. Part 2 of 5 Given that the restaurant is located in the Southeast, the probability that it is in a city with a population under 50,000 is Part 3 of 5 Given that the restaurant is located in the Southwest, the probability that it is in a city with a population of 500,000 or less is Part 4 of 5 Given that the restaurant is located in a city with a population of 500,000 or less, the probability that it is in the Southwest is Part 5 of 5 Given that the restaurant is located in the South (either SE or SW), the probability that it is in a city with a population of 50,000 or more isGenetics: 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. Gene 2 Dominant Recessive Dominant S7 2? Gene 1 Recessive 10 6 Send data to Ema! (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? ([1) 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 D . New car: At a certain car dealership, the probability that a customer purchases an SUV is {115. Given that a customer purchases an SUV, the probability that it is black is 0.23. What is the probability that a customer purchases a black SUV? Round your answer to four decimal places, if necessary. The probability that a customer purchases a black SUV is D. Defective components: A lot of 10 components contains 3 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. (a) Find P (A). (b) Find P (B | A). (c) Find P (A and B). (d) Are A and B independent? Explain. Part: 0 / 4 Part 1 of 4 Find P (A) = OO X 5