Basic Questions: probability I'll be able to go on walk on given weekend day?

[Maxik]

As the title says, I have some basic questions.

Say I have worked out that, on a given day, the probability of rain is 0.6. Now I love going on walks, but I can only go when it rains and on weekends. What is the probability I'll be able to go on a walk on a given weekend day? Intuitively I'd say the probability is the same as above, but my intuition always fails dramatically when it comes to probability calculations. Or is it *2/7?

Having worked out said probability, I then want to know on how many days, approximately, I'll be able to go on a walk each year. Do I just take the probability - let's call it P - and work out P*2/7*365.25?

Help would be very much appreciated.

 

[Quick]

The way I would look at this problem is to try and figure out how many weekends there are in a year first.

Then I would multiply my probability by that.

But I am not a mod here and my math skills are not that great, so see what the mods have to say.

 

[Dr.Peterson]

Say I have worked out that, on a given day, the probability of rain is 0.6. Now I love going on walks, but I can only go when it rains and on weekends. What is the probability I'll be able to go on a walk on a given weekend day? Intuitively I'd say the probability is the same as above, but my intuition always fails dramatically when it comes to probability calculations. Or is it *2/7?

Having worked out said probability, I then want to know on how many days, approximately, I'll be able to go on a walk each year. Do I just take the probability - let's call it P - and work out P*2/7*365.25?

The question needs clarification. (Often the reason one's intuition fails is that one has not defined the problem clearly.)

You ask, "What is the probability I'll be able to go on a walk on a given weekend day?" I would take this to mean, today is a Saturday or Sunday; what is the probability that it is raining? Given that you've found that the probability of rain on any given day of the year is 0.6, then the answer is just 0.6! That's the probability of rain on any day, which applies

If what you meant was really, "What is the probability I'll be able to go on a walk on at least one of the two days this weekend (that is, either next Saturday or Sunday)?", then there is a way to do that, but I'll hold off on telling you until we know if that's what you mean.

It's also uncertain what you mean by, "I can only go when it rains and on weekends". As a mathematician, I would take this to mean "I can only walk when it is raining and it is a weekend"; that is, I can't walk if it is not raining, even if it is a weekend, and I can't walk during the week, even if it is raining". But you might have intended something else, such as that you can only walk when it is either raining, or a weekend. Not to mention that it seems odd that you would walk only in the rain.

Now you ask, "on how many days, approximately, I'll be able to go on a walk each year." We can take it this way: about 2/7 of the days in the year are on weekends; on average, you can walk on 0.6 of those; so, yes, the average number of weekend days with rain in any given year is 365.25 * 2/7 * 0.6 = 62.6 days. And, yes, 365 * 2/7 is the number of weekend days (not weekends) there are in the year, so Quick is not too far off (if we're interpreting the question correctly). If you are asking about this year, you would want to count the weekend days this year, rather than approximation with 365.25 and 2/7.