Question

probability distribution
(axes and bars with labels no prize, 1st, 2nd, 3rd, 4th)
probability distribution
(axes and bars with labels no prize, 1st, 2nd, 3rd, 4th)

Explanation:

Step1: Analyze Probability Distribution Properties

In a valid probability distribution, the sum of all probabilities must equal 1 (or 100% if in percentage terms). For a bar graph (probability mass function for discrete data), the heights (probabilities) of all bars should sum to 1.

Step2: Evaluate the First Graph

The first graph has a bar for "No Prize" with a height (probability) that looks much larger (e.g., around 35 - 40 if we assume the y - axis is in percentage, but even visually, the other bars are very small, but the sum of percentages would likely exceed 100% or the sum of probabilities would exceed 1 if we consider the y - axis scale).

Step3: Evaluate the Second Graph

The second graph has a "No Prize" bar with a height (probability) around 0.8, and the other bars (for 1st, 2nd, 3rd, 4th) have small heights. When we sum these probabilities, the total is likely to be 1 (since the "No Prize" is a large portion, and the rest are small, but their sum with 0.8 is 1). In a probability distribution, the total probability must be 1. So the second graph (the lower one) is a valid probability distribution.

Answer:

The lower (second) Probability Distribution graph