A soft-drink manufacturer is running a marketing promotion exercise for a new drink in which a gold star is stamped on the inside of the top of 1 in 20 bottles. The gold star entitles the purchaser to claim a cash gift from the manufacturer.Consider a person who buys 20 bottles of the soft drink over the promotion period.Let X be the random variable for the number of gold star tops that the person will get from these 20 bottles.For each question below, pick the formal probability statement that is equivalent to the probability required. Note that in some cases you will have to think about how the complement rule would be used to calculate the required probability.The probability that the person will get no gold star tops from these 20 bottles.Answer 1The probability that the person will get less than 2 gold star tops from these 20 bottles.Answer 2The probability that the person will get more than 1 gold star top from these 20 bottles.Answer 3

On a popular app, users rate hair salons as 1, 2, 3, 4, or 5 stars. Suppose a rating is randomly selected from all the ratings on the app. Let X be the number of stars of the selected rating. Here is the probability distribution of X.Value x of X 1 2 3 4 5P=Xx 0.24 0.20 0.09 0.20 0.27For parts (a) and (b) below, find the probability that the randomly selected hair salon rating has the described number of stars.(a) 4 or more:(b) Fewer than 3:

A food truck sells tacos, burritos, and drinks.Let event A = A customer buys a taco.Let event B = A customer buys a drink.What does P(A or B) = 0.45 mean in terms of this problem?A.The probability that a customer buys both a taco and a drink is 45%.B.The probability that a customer buys neither a taco nor a drink is 45%.C.The probability that a customer buys a taco, a drink, or both is 45%.D.Buying a taco and buying a drink are mutually exclusive events.

A company has both male and female employees. The company has shirts and jackets with the company logo to give away to employees. For each of the company's 215 employees, a manager asked which piece of clothing the employee prefers. The preferences, based on gender, are summarized in the table below.ShirtJacketMale54 69Female79 13Suppose an employee of the company is chosen at random.Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.(If necessary, consult a list of formulas.)(a)What is the probability that the employee prefers a jacket?(b)What is the probability that the employee is male or prefers a jacket?

A bag contains blue and pink raffle tickets. What is the complement of selecting a blue raffle ticket if the probability of selecting a pink raffle ticket is 0.23?

Question 2In a group of students 25% are enrolled in physics, 23% in sociology, 17% in chemistry, 14% in political science, 12% in anthropology, and 9% in math. You are going to select an individual from the group of students. The probability of event A is equivalent to the probability that you select someone who studies social science (sociology, political science and anthropology) or physics. What is the probability of the event A’s complement?1 point0.510.260.490.74