The following table represents undergraduate students at a local university. One student is chosen at random. Give your answer as a decimal out to at least 4 places. Freshman Sophomore Junior Senior Total Live On Campus 2294 2188 1724 1888 8094 Live Off Campus 3831 4286 4925 822 13864 Total 6125 6474 6649 2710 21958 a) Find the probability that the student lives off campus or is a junior. b) Find the probability that the student lives on campus and is a senior. c) Find the probability that the student is a freshman given that they live on campus. d) Are the events Freshman and Live on Campus mutually exclusive? Why? Yes, since the P(Freshman | Live On Campus) = P(Freshman) Yes, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ 0 No, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ 0 Yes, since you can be a freshman that lives on campus No, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ P(Freshman)*P(Live On Campus) = 0.1028 Yes, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ P(Freshman)*P(Live On Campus) = 0.1028 e) Are the events Freshman and Live on Campus independent? Why? Yes, since the P(Freshman | Live On Campus) = P(Freshman) Yes, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ 0 No, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ 0 Yes, since you can be a freshman that lives on campus No, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ P(Freshman)*P(Live On Campus) = 0.1028 Yes, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ P(Freshman)*P(Live On Campus) = 0.1028
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.
The following table represents undergraduate students at a local university. One student is chosen at random. Give your answer as a decimal out to at least 4 places.
| Freshman | Sophomore | Junior | Senior | Total | |
| Live On Campus | 2294 | 2188 | 1724 | 1888 | 8094 |
| Live Off Campus | 3831 | 4286 | 4925 | 822 | 13864 |
| Total | 6125 | 6474 | 6649 | 2710 | 21958 |
a) Find the probability that the student lives off campus or is a junior.
b) Find the probability that the student lives on campus and is a senior.
c) Find the probability that the student is a freshman given that they live on campus.
d) Are the
- Yes, since the P(Freshman | Live On Campus) = P(Freshman)
- Yes, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ 0
- No, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ 0
- Yes, since you can be a freshman that lives on campus
- No, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ P(Freshman)*P(Live On Campus) = 0.1028
- Yes, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ P(Freshman)*P(Live On Campus) = 0.1028
e) Are the events Freshman and Live on Campus independent? Why?
- Yes, since the P(Freshman | Live On Campus) = P(Freshman)
- Yes, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ 0
- No, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ 0
- Yes, since you can be a freshman that lives on campus
- No, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ P(Freshman)*P(Live On Campus) = 0.1028
- Yes, since P(Freshman ∩∩ Live On Campus) = 0.1045 ≠ P(Freshman)*P(Live On Campus) = 0.1028
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