To determine the missing probability [tex]\( P(4) \)[/tex] for the given discrete probability distribution, follow these steps:
1. Understand the Requirement:
The sum of all probabilities in a discrete probability distribution must equal 1. This ensures that we account for all possible outcomes.
2. List the Given Probabilities:
We are given the following probabilities:
- [tex]\( P(3) = 0.19 \)[/tex]
- [tex]\( P(5) = 0.35 \)[/tex]
- [tex]\( P(6) = 0.17 \)[/tex]
3. Calculate the Sum of the Given Probabilities:
Add the probabilities provided:
[tex]\[
P(3) + P(5) + P(6) = 0.19 + 0.35 + 0.17 = 0.71
\][/tex]
4. Determine the Missing Probability:
Subtract the sum of the given probabilities from 1. This will give us the probability for the missing event, [tex]\( P(4) \)[/tex]:
[tex]\[
P(4) = 1 - \left( P(3) + P(5) + P(6) \right) = 1 - 0.71 = 0.29
\][/tex]
Thus, the missing probability [tex]\( P(4) \)[/tex] is [tex]\( 0.29 \)[/tex].
In summary:
[tex]\[
P(4) = 0.29
\][/tex]
The sum of the given probabilities is [tex]\( 0.71 \)[/tex].
This completes the solution to determine the missing probability [tex]\( P(4) \)[/tex] to make the given distribution a complete discrete probability distribution.
