a) How many positive three-digit integers are multiples of 7? (b) What is the probability that a randomly chosen positive three-digit integer is a multiple of 7? (c) What is the probability that a randomly chosen positive three-digit integer is a multiple of 6? Suppose that on a true/false exam you have no idea at all about the answers to three questions. You choose answers randomly and therefore have a 50–50 chance of being correct on any one question. Let CCW indicate that you were correct on the first two questions and wrong on the third, let WCW indicate that you were wrong on the first and third questions and correct on the second, and so forth. (a) List the elements in the sample space whose outcomes are all possible sequences of correct and incorrect responses on your part. (b) Write each of the following events as a set, in set-roster notation, and find its probability. (i) The event that exactly one answer is correct. set = .........?probability = .................? (ii) The event that at least two answers are correct. set = ................? probability = ..................? (iii) The event that no answer is correct. set = ..................?probability = ...............? Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children. Let BBG indicate that the first two children born are boys and the third child is a girl, let GBG indicate that the first and third children born are girls and the second is a boy, and so forth. (a) List the eight elements in the sample space whose outcomes are all possible genders of the three children. (b) Write each of the following events as a set, in set-roster notation, and find its probability. (i) the event that exactly one child is a girl set = ................?probability = ...............? (ii) the event that at least two children are girls set = .............?probability = ..............? (iii) the event that no child is a girl set = ................?probability = .................?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
probability = .................?
probability = ...............?
probability = ...............?
probability = ..............?
probability = .................?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
