(1.) Let assume that a traveler is planning to travel to an exotic destination for her/his summer vacation. However, for the destinations she/he is considering there is a risk of contracting either A type illness or B type illness. These are generally contracted after ingesting contaminated water or food, and in their onset have similar symptoms. The center for disease control has collected traveler data for her/his destination. Based on that data, the probability a traveler will get A type illness and not get B type illness 0.05. The probability a traveler will get B type illness and not get A type illness is 0.3. Finally, the probability a traveler will get both diseases is 0.01. Let A denote the event a traveler gets A type illness s, and B denote the event a traveler gets B type illness. (a) Compute the probability a traveler will get A type illness (that is compute P(A)). (b) Compute the probability a traveler will be ill (which means she contracted at least one of the diseases). (c) Are the events A and B independent? (d) A traveler is showing the first symptoms of these diseases, indicating she/he has either A type illness or B type illness. Given that the traveler is sick, what is the probability he contracted both diseases.
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.
(1.) Let assume that a traveler is planning to travel to an exotic destination for her/his summer vacation. However, for the destinations she/he is considering there is a risk of contracting either A type illness or B type illness. These are generally contracted after ingesting contaminated water or food, and in their onset have similar symptoms. The center for disease control has collected traveler data for her/his destination. Based on that data, the
(a) Compute the probability a traveler will get A type illness (that is compute P(A)).
(b) Compute the probability a traveler will be ill (which means she contracted at least one of the diseases).
(c) Are the events A and B independent?
(d) A traveler is showing the first symptoms of these diseases, indicating she/he has either A type illness or B type illness. Given that the traveler is sick, what is the probability he contracted both diseases.
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