Conditional probability (reduced sample space) a) Among a group of 500 pet owners who visit the same pet store, it is found that 345 have a cat, while 375 have a dog. There are 290 of these who have both a dog and a cat. Suppose one individual is chosen at random from this group of 500 pet owners. Find the conditional probability the individual has a dog given that he or she has a cat. b,c) [use two way table from previous problem] Conditional Probability and Reduced Sample Space Consider the following two-way table representing the weather at a certain location on 300 days No Rain Little Rain (<1 in) Rain (>1 in) Sunny 175 15 0 190 Cloudy 43 32 35 110 218 47 35 300 Find each of the probabilities b) Probability of no rain given that it is a sunny day, Pr(No Rain | Sunny) c) Probability of a sunny day given that there is no rain, Pr (Sunny | No Rain)
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.
Conditional probability
(reduced sample space)
a)
Among a group of 500 pet owners who visit the same pet store, it is found that 345 have a cat, while 375 have a dog.
There are 290 of these who have both a dog and a cat.
Suppose one individual is chosen at random from this group of 500 pet owners.
Find the conditional probability the individual has a dog given that he or she has a cat.
b,c) [use two way table from previous problem]
Conditional Probability and Reduced Sample Space
Consider the following two-way table representing the weather at a certain location on 300 days
| No Rain | Little Rain (<1 in) | Rain (>1 in) | ||
| Sunny | 175 | 15 | 0 | 190 |
| Cloudy | 43 | 32 | 35 | 110 |
| 218 | 47 | 35 | 300 |
Find each of the probabilities
b) Probability of no rain given that it is a sunny day, Pr(No Rain | Sunny)
c) Probability of a sunny day given that there is no rain, Pr (Sunny | No Rain)
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