probability questions

[/0]

"Given the number of days in a month is 30, what is the probability that the number of letters in the name is less than or equal to 6?"

Do they seem like dependent or independent events? How can you tell quickly?

[Mao]

April, June, September, November
Pr = 0.5
...? [I don't see any other way of doing it..]

[/0]

Hmm it's just that the book I'm using says that they are independent events, but intuitively they seem to be dependent... i.e. the information in the first clause 'seems' to help you identify a more accurate probability.

Apart from evaluating I wouldn't have known they were independent events, would you?

[/0]

Also, I'm having trouble with this problem:

"The future lifetimes (in months) of two components of a machine have the following joint density function.



What is the probability that both components are still functioning 20 months from now?"

The answer is 0.008 but I get 0.424 :O

Is my area interpretation correct?

thanks

[Mao]

White: 0< x < 20, 0 < y < 20
Green: 0< x < 20, 20 < y < 50
Blue: 20 < x < 50, 0 < y < 20
Red: 20 < x, 20 < y

You can see that green and blue does not meet the conditions of x > 20, y > 20, hence only red is the region required

[/0]

thanks maaaoooo!

[/0]

There's a proof in the book that and it involves the step:



I don't get how that works though.... how does it simplify?

Here's the proof: