So my teacher asked me this question. What is the probability that someone chooses Friday (or any other day for that matter) in the month of July. I thought about it but it doesn't look that easy.
I got a 52/217 by adding 1/7 and 3/31. Can you please help?
The choice of all days is all days of the week.
And my calculation does not have a logic. That is what I need.
The only thing is I got it this way.
First I took February which has 28 days. The probability becomes 1/7.
Then I took February in a leap year and I thought the probability should become 2/7 (because of an extra day).
But then I assumed a month with 35 days. According to my logic it would mean 1/7 + 7/7 (because of the 7 extra days) which would be wrong.
Basically my calculation is wrong probably.
Best Answer
The question as you have asked it is ambiguous. The fundamental idea of probability theory is you need to specify what are the objects you are choosing from (with all choices equally likely), and which choices are considered "desirable".
You are choosing a random day in a specific July, e.g. July 2014, and want to know the probability it's Friday. Then you count the number of Fridays and divide by the number of days in that month, to get $\frac{4}{31}$.
You are choosing a random day in the year, e.g. 2014, and want to know the probability it's a Friday in July. Then you count the number of Fridays in July and divide by the number of days, to get $\frac{4}{365}$.
You are choosing what to eat for breakfast, and want to know the probability that you pick a Friday in July. Then the answer is $0$.
The only time you would add probabilities, as in the OP, is if you are adding the probabilities of disjoint events. For example, if Event 1 is as in #1, and Event 2 is choosing a Tuesday in July 2014. Event 1 is $\frac{4}{31}$ while Event 2 is $\frac{5}{31}$, so the probability of choosing a (Friday or Tuesday) is $\frac{4}{31}+\frac{5}{31}=\frac{9}{31}$.