Calculating Probability of Snow in Exactly One of Two Cities

In summary, the probability of snowing in exactly one of the two cities, assuming independence, is 0.4896. This is calculated by taking the sum of the probabilities of snow in one city and not the other, and subtracting the probability of snow in both cities. However, as the events are mutually exclusive, the last calculation is not necessary. The final answer is correct, but part marks may be deducted.
  • #1
BrownianMan
134
0
I had this question on a test:

The probability of snowing in one city is 0.4, and the probability of snowing in another city is 0.7. Assume independence. What is the probability that it snows in exactly one of the two cities?

The way I approached it was to say that the probability that it snows in exactly one of the two cities is:

Let A denote probability of snow in the first city.
Let B denote probability of snow in the second city.

P(A and 'not B') or P('not A' and B) = (0.4)(0.3) + (0.6)(0.7) - (0.4)(0.3)(0.6)(0.7) = 0.4896

Is this correct?
 
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  • #2
I don't think you need that part you are subtracting.
 
  • #3
Yeah, I just realized that. The events P(A and 'not B') and P('not A' and B) are mutually exclusive.

The question was out of 6, so at least I'll get part marks.
 

FAQ: Calculating Probability of Snow in Exactly One of Two Cities

What exactly is a probability test question?

A probability test question is a type of question that assesses the likelihood or chance of a certain event occurring. It is used in various fields such as mathematics, statistics, and science to measure the understanding and application of probability concepts.

What are the different types of probability test questions?

There are several types of probability test questions, including multiple-choice, true/false, and open-ended questions. Multiple-choice questions present a statement or question with several possible answers, while true/false questions require a simple "true" or "false" response. Open-ended questions allow for a more detailed explanation or calculation of the probability.

How do I approach solving a probability test question?

The first step is to carefully read and understand the question and the given information. Then, identify the type of question and use the appropriate formula or method to solve it. It is important to show your work and explain your reasoning to receive full credit.

What are some common mistakes to avoid when answering probability test questions?

One common mistake is to confuse the probability of an event with the odds of that event. Remember that probability is the likelihood of an event occurring, while odds are the ratio of favorable outcomes to unfavorable outcomes. Another mistake is to assume that all events have an equal chance of occurring, when in reality, some events may be more likely than others.

How can I improve my performance on probability test questions?

Practice is key to improving your understanding and performance on probability test questions. You can also review probability concepts and formulas regularly, and seek help from a teacher or tutor if needed. Additionally, pay attention to the language used in the question and carefully read all given information to avoid making careless mistakes.

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