To determine which option represents a uniform probability distribution, we need to understand what a uniform probability distribution is.

A uniform probability distribution is a distribution where all outcomes in the sample space are equally likely to occur. In other words, each possible outcome has the same probability of happening.

Let’s analyze each option:

1. “The probability of reaching a temperature of 75°F on any given day of the year in St. Louis, MO”: This is unlikely to be a uniform probability distribution because the temperature on any given day is influenced by various factors, such as the time of year, weather patterns, and climate conditions. The probability of reaching 75°F is not the same for every day of the year.
2. “A time period in which it rained 25% of the time and did not rain 75% of the time”: This option does not represent a uniform probability distribution because the probabilities of raining (0.25) and not raining (0.75) are not equal.
3. “The probabilities of drawing any individual card in a deck with one draw”: This represents a uniform probability distribution. In a standard deck of 52 cards, each card has an equal probability of being drawn with a single draw (1/52).
4. “Flipping a coin two times and recording whether heads or tails”: This represents a uniform probability distribution. When flipping a fair coin twice, there are four possible outcomes: HH, HT, TH, and TT, and each outcome has an equal probability of occurring (1/4).

Therefore, the options that represent a uniform probability distribution are “The probabilities of drawing any individual card in a deck with one draw” and “Flipping a coin two times and recording whether heads or tails.”