Option C) x 1 2 3 4; p 0.4 0.25 0.2 0.15 is the correct probability distribution table because each probability is between 0 and 1 and their sum equals 1.
When identifying a probability distribution table, we need to check two main conditions:
Each probability value (P(x)) must be between 0 and 1.
The sum of all the probabilities in the table should equal 1.
Looking at the given options:
A) has negative probabilities, which is not valid.
B) seems to have probabilities between 0 and 1, and their sum is 0.95, which is close but not exactly 1.
C) has probabilities between 0 and 1 and their sum equals 1. So, this is a valid probability distribution.
D) has a probability greater than 1, which is not possible.
Only option C) x 1 2 3 4; p 0.4 0.25 0.2 0.15 satisfies both conditions and is therefore the correct probability distribution table.