For eachrexperiment, determine whether events A and B are independent or dependent. Experiment Events Independent Dependent A bean is randomly selected from a bag containing red beans and white beans and eaten. Then another random selection is made from the remaining beans. Event A: The first selection is a white bean. Event B: The second selection is a red bean. A deck contains 8 cards numbered 1 through 8. A card is randomly chosen from the deck. The card is then put back into the deck. The deck selected is numbered is shuffled. Then another randóm selection is made. Event A: The first card 4. Event B: The second card selected is numbered 5. A number cube with sides labeled 1 through 6 is rolled. Then a spinner with slices numbered 1 through 9 is spun. Event A: The number cube roll is an even number. Event B: The spinner lands on an odd number. A bin contains marbles numbered 1 through 9. A marble is randomly selected from the bin and returned to the bin. The marbles are mixed. Then another random selection is made. Event A: The first selection is an odd numbered marble. Event B: The second selection is an even numbered marble. A family has two children. Event-A: The ölder child is a boy. Event B: Both children are boys.
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.
Two events are said to be independent if the occurrence of one event does not affect the probability of occurrence of the other event.
Two events are said to a dependent if the occurrence of one event affects the probability of occurrence of the other event.
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