combinatory & probability

0 is EVEN !!! I didn't know that ! Helpful post indeed !

(D) 15/16

P(at least one even) = 1 - P(no one even)
= 1 - (4*4*4*4)/(8*8*8*8)
= 1 - 1/(2*2*2*2)
= 1 - 1/16
= 15/16

15/16 is right answer, I forgot to do (1/2)(1/2)(1/2)(1/2) four times as the key is 4 digits.
(1/2) is the probability that the digit will be odd. So 1 - [(1/2)raise to 4] is teh required probability.

The point with this question is to remember that you have 8 possible numbers which 4 of them are even.
the Pass code can be 3333, I mean you can have all 4 digits the same numbers too.
1-(1/4)^4=15/16

1- Prob of selecting 3,5,7,9 out of ( 2,3,5,6,7,8,9,0) at four places

1- (1/2 * 1/2 * 1/2 * 1/2)

1- 1/16

= 15/16
D

Lifetron wrote:0 is EVEN !!! I didn't know that ! Helpful post indeed !

This is one of the least known of the crucial GMAT facts, in my experience. Definitely remember this on test day!

Other crucial properties of 0:

* It isn't prime
* It's neither negative nor positive
* It belongs to the set of nonnegative numbers, so any time you see the phrase 'nonnegative', think of 0
* 0! = 1
* x� = 1, unless x = 0 itself, since 0� is undefined
* It's a multiple of every integer
* It only has one multiple (itself)
* It isn't a factor of ANY integer
* It has every integer other than itself as factors

I think 0^0 means 1 . Also in general terms anything have power 0 is 1

check below link

https://www.askamathematician.com/2010/1 ... -disagree/

Nope, it's undefined. Punch in 0� at Wolfram and see what you receive.

One of the simpler arguments for this is that the familiar proof that x� = 1 depends on division: x¹ / x¹ = 1, but x¹ / x¹ also = x�. Hence x� = 1. But you can't divide by 0, so x ≠ 0. This doesn't mean that 0� ≠ 1, it just means that we can't establish such an identity this way.

There are better, more involved arguments that you can read if you're curious. The gist is that in real analysis, the 'same logic' that gives 0� = 1 also can give 0� = 0, so 0� is left undefined.