An experiment has seven equally likely outcomes: E1, E2, E3, E4, E5, E6, and E7. Round your answers to three decimal places. a. What is the probability that E2 occurs? b. What is the probability that any two of the outcomes occur (e.g. E1, or E3)? c. What is the probability that any three of the outcomes occur (e.g. E1, or E2 or E4)?
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. An experiment has seven equally likely outcomes: E1, E2, E3, E4, E5, E6, and E7. Round your answers to three decimal places.
a. What is the
b. What is the probability that any two of the outcomes occur (e.g. E1, or E3)?
c. What is the probability that any three of the outcomes occur (e.g. E1, or E2 or E4)?
2. Five observations taken for two variables follow.
| 4 | 5 | 11 | 4 | 13 | |
| 40 | 40 | 40 | 50 | 20 |
A. Compute the sample
B. Compute the sample
C. What can you conclude, based on your computation of the sample correlation coefficient?
3. Suppose that at the beginning of Year 1 you invested in the Stivers mutual fund and in the Trippi mutual fund. The value of each investment at the end of each subsequent year is provided in the table below.
| Year | Stivers | Trippi |
| Year 1 | $10,500 | $5,600 |
| Year 2 | $11,800 | $6,400 |
| Year 3 | $13,000 | $6,900 |
| Year 4 | $14,000 | $7,700 |
| Year 5 | $14,900 | $8,600 |
| Year 6 | $16,100 | $9,200 |
| Year 7 | $17,000 | $9,900 |
| Year 8 | $18,200 | $10,600 |
Compute the mean annual return for the Stivers mutual fund and for the Trippi mutual fund. Do not round intermediate calculations.
| Stivers | Trippi | |||
| Mean annual return (to decimals) |
Which mutual fund performed better?
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