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Magazine Chapter 4: Q15E (page 223)
A die is tossed. Let x be the number of spots observed on the upturned face of the die.
a. Find the probability distribution of x and display it in tabular form.
b. Display the probability distribution of x in graphical form.
Short Answer
a.
| x | 1 | 2 | 3 | 4 | 5 | 6 |
| P(x) | \(\frac{{\rm{1}}}{{\rm{6}}}\) | \(\frac{{\rm{1}}}{{\rm{6}}}\) | \(\frac{{\rm{1}}}{{\rm{6}}}\) | \(\frac{{\rm{1}}}{{\rm{6}}}\) | \(\frac{{\rm{1}}}{{\rm{6}}}\) | \(\frac{{\rm{1}}}{{\rm{6}}}\) |
b.
Step by step solution
Definition of a fair die
A fair die has six sides containing numbers from 1 to 6 and is often used in different types of games.The probability of the occurrence of a number is equal since all the numbers have an equal chance of appearing once the die is tossed.
Definition of a probability distribution
The calculation of the probability of each number is shown below:
The probability of all the numbers will be. Based on this data the relevant table is shown below:
| x | 1 | 2 | 3 | 4 | 5 | 6 |
| P(x) |
Definition of probability distribution
The probability distribution is a theory often used by researchers while doing statistical analysis.For a particular data generating process, the researchers try to find out anticipate the outcomes for a particular set of values.
Graphical representation
Since the probability of all the values is equal to one-sixth, the size of the bars will be equal as shown in the probability distribution graph below:
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