Question3 a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product. i. Define the variable of interest for this scenario. ii. What probability distribution do you think best describes the situation? Why? iii. Calculate the probability that exactly 9 will buy the product. iv. If 80 persons are introduced to the product, determine the number of person who are expected to buy the product. b) It is known that an average of 5 trains pass through Grand Central Terminal every 30 minutes. Find the probability that i. Exactly 4 trains will pass in 30 minutes ii. less than 2 trains will pass in an hour
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Question3
a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product.
i. Define the variable of interest for this scenario.
ii. What probability distribution do you think best describes the situation? Why?
iii. Calculate the probability that exactly 9 will buy the product.
iv. If 80 persons are introduced to the product, determine the number of person who are expected to buy the product.
b) It is known that an average of 5 trains pass through Grand Central Terminal every 30 minutes. Find the probability that
i. Exactly 4 trains will pass in 30 minutes
ii. less than 2 trains will pass in an hour
Step by step
Solved in 2 steps with 2 images
