First six positive integers are 1, 2, 3, 4, 5, 6.
If three numbers are selected at random from above six numbers then the sample space S have 20 elements as
Here X, greatest of the three numbers obtained, is random variable. X may have value 3, 4, 5, 6. Therefore required probability distribution is given as
P(X = 3) = Probability of event getting 3 as greatest number.
P(X = 4) = Probability of event getting 4 as greatest number.
P(X = 5) = Probability of event getting 5 as greatest number.
P(X = 6) = Probability of event getting 6 as greatest number.
Required probability distribution in tabular form as
| X or xi |
3 |
4 |
5 |
6 |
| P(X) or pi |
\(\frac{1}{20}\) |
\(\frac{3}{20}\) |
\(\frac{6}{20}\) |
\(\frac{10}{20}\) |
