Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather had the following distribution:

Event Relative Frequency
Clear & dry 0.20
Cloudy & dry 0.30
Rain 0.40
Snow 0.10

Supposing next Christmas is dry, determine the probability that it will also be cloudy.

Question

Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather had the following distribution:

Event	Relative Frequency
Clear & dry	0.20
Cloudy & dry	0.30
Rain	0.40
Snow	0.10

Supposing next Christmas is dry, determine the probability that it will also be cloudy.

BlackTom AI · Accepted Answer

Let's break down the problem and examine what is being asked. We are told that next Christmas is dry, and we want the probability that it will also be cloudy. This is a conditional probability problem.
Option A: 0.60 — This value corresponds to P(Cloudy | Dry) = P(Cloudy and Dry) / P(Dry) = 0.30 / (0.20 + 0.30) = 0.30 / 0.50 = 0.60. This aligns with the definition of conditional probability when the condition is that the day is dry and we look for the likelihood of cloudiness.
Option B: 0.45 — If someone computed P(Cloudy | Dry) as 0.45, they might have miscounted the denominator or numerator, perhaps using 0.30 / 0.666... or mixing up categories. However, the correct denominator for Dry is the sum of all dry scenarios (Clear & dry and Cloudy & dry), which is 0.50, not 0.666...
Option C: 0.70 — A value this high would imply a much larger share of dry days are cloudy, which contradicts the given frequencies. Since only 0.30 of the total 0.50 dry fraction is Cloudy & Dry, 0.70 would require inconsistency with the data, making this option incorrect.
Option D: 0.50 — This would happen if one mistakenly used P(Dry) = 0.50 as the probability but interpreted it as the conditional probability rather than the ratio 0.30 / 0.50. The actual conditional probability is the ratio of the cloudy-and-dry portion to all dry days, not simply 0.50. Therefore this choice misapplies the concept.
To summarize, the correct approach is to use the conditional probability formula with the provided dry day breakdown, yielding 0.60, while the other options arise from misapplication or miscalculation of the conditioning information.

OSC 2030-009 Fall 2025 SUBMIT: Graded Homework Module 3 (Chap 4)

Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather had the following distribution: Event Relative Frequency Clear & dry 0.20 Cloudy & dry 0.30 Rain 0.40 Snow 0.10 Supposing next Christmas is dry, determine the probability that it will also be cloudy.

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