Question

A weather station in a major city in the Northwest kept data about the weather conditions over the past year. The probabilities are displayed in the table below:


Hot Mild Cold
Sunny 0.15 0.30 0.10
Cloudy 0.10 0.25 0.10


If a random day is chosen from this data, what is the probability that the day was hot or sunny?
@mathmale

Answer 1

As much as I'd like to help you with this right now, I have another student on hold (a long hold). But you know enuf from our previous discussion how to add up all the rows and columns; do that same with this new table as you did last time. Note that the total probability must be 1.00.

I will help if I can but please let others help if they know the material and care to step in.

Answer 2

See what you can transfer from out previous discussion to this problem. Note that in this problem you have an OR and will need to add together two probabilities to obtain the final answer.

Answer 3

Here's the same table:

Hot Mild Cold
Sunny 0.15 0.30 0.10
Cloudy 0.10 0.25 0.10

Here are the instructions: "If a random day is chosen from this data, what is the probability that the day was hot or sunny?"

Important: add up those 6 probabilities. You'll find that their sum is 1.00.

Answer 4

OK: what fraction of those days were hot? Add 0.15 and 0.10; result: 0.25.
What fraction of those days were sunny? Add together: 0.15, 0.30, 0.10.

What fraction of those days were BOTH hot and sunny? Look in the HOT column and the SUNNY row. What fraction do you see where this column intersects this row?


The probability that the day you pick at random was hot OR sunny (but not both), is

P(hot) + P(sunny) - P(both hot and sunny).

See if you can pick out the right numerical values to enable you to evaluate this formula.

then you're done!

Answer 5

EXCEPT: ;( there's more to learn about this contingency table and about conditional probability, so this one example, while helpful, is not sufficient. I suggest you find and post more such problems; then you and I , or you and others, could practice further.

Answer 6

If you decide to take this problem all the waY to completion, plese share at least some of your work with me, so that I'll know how you arrived at your answer.

Answer 7

is it .3? @mathmale

Answer 8

Aw, come on, woohoo! In my very last comment i asked you to share your work with me, so that I'd know how you got your answer. woohoo!!??

Answer 9

I get 0.65.

How? The probability that any given day chosen at random is hot is 0.25.

the probability that any given day chosen at random is sunny is 0.55.

Adding those together results in 0.80.

the probability that any given day will be BOTH hot and sunny is 0.15. Take a look at the table, above.

Subtract this 0.15 from 0.80. what's the result? that's the answer you wanted.
This is what I'd like you to share with me wen you want me to check an answer. You don't need all that detail, but at least some would be welcomed and appreciated.

Answer 10

so the probability that any given day chosen at random will be hot OR sunny is 0.65.

Answer 11

sorry ok i will. I can't Thank You enough!

Answer 12

I'm so glad I could be of help. Sorry I've annoyed you with my often slow respones. It's either read the paper or a book while waiting for you, or help someone else until I see that you've responded.... more often than not I go on to help others. I'm not a student myself, but rather a retired math teacher with 43 years of experience.

Answer 13

.65 is absolutely the correct answer!