A jar contains red, yellow, and green marbles. Based on what you see in the jar you feel that the P(yellow) = 1/3. What type of probability is illustrated and why?

This is an example of subjective probability because it is based on personal judgment or a subjective assessment of the likelihood of an event occurring. The probability is not based on any objective data or calculation but rather on the observer's intuition or perception.

The type of probability illustrated in this case is subjective probability. Subjective probability is based on personal judgment or opinion and is not calculated using a formal mathematical approach. In this case, the statement "P(yellow) = 1/3" is the subjective probability as it is based on what the individual perceives from looking at the jar. It is not obtained by conducting a rigorous statistical analysis or by counting the number of marbles of each color in the jar.