Hello again, maths2008!

So there are *four* stations. Code:

* - - - - - * - * - - - - - - *
1 2 3 4

We cannot make the trip if one or more stations are closed.

The only way to *make* the trip is when *all four stations are open.*

Let be the probability that a station is open.

The probability that all four stations are open is:

. . and we want this probability to be __greater__ than one-half.

So we have: .

Hence: .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

You can solve the problem "head on" if you dare.

But there are **fifteen** cases you must consider . . .

. .

. . . . .