Riddles, brain puzzles and mathematical problems

[Bridge]

Does the switch being open mean a current can pass through it?

Anyway, BAndrew, why are you subtracting the possibility of all of the switches being open? Shouldn't that be added to the other possibilities? So:

(1/3)^3+(1/3)^2+(1/3)^5 = 0,152

[Froge]

Does the switch being open mean a current can pass through it?

Uh....no. It's the exact opposite. A closed switch means a current can pass through it.

None of you are correct yet, not even in methodology.

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Next question:



This crudely drawn circuit has 3 switches on top and 2 at bottom. The probability that any switch is open is 1/3.



Find the probability that a current can travel across this circuit.

I don't quite understand the drawing... Is the negative pole supposed to be on the left and the positive pole on the right?
In that case I think one would have to add the probability of the upper line being closed and that of the lower line being closed:

upper line:
2/3 x 2/3 x 2/3 = 8/27

lower line:
2/3 x 2/3 = 4/9 = 12/27

makes 20/27 or ~0,740 (period)

Both lines being closed should already be included in that I think...

That seems way too easy though... so I'm probably wrong or I misunderstood something

[Statyk]

Next question:

This crudely drawn circuit has 3 switches on top and 2 at bottom. The probability that any switch is open is 1/3.

Find the probability that a current can travel across this circuit.

The question does not state if switches are shut... Are we including these as possibly being closed switches?

If all switches are open... there is no circuit and 0% probability. So I may just have my points wrong here... 0% probability doesn't seem right.

[xxxxxxxxxxxxxxxx]

The question does not state if switches are shut... Are we including these as possibly being closed switches?

I think the five switches seen in the picture each simply have a probability of 1/3 to be open and 2/3 to be closed everytime you start the current. Closed switch means current can travel over it.

[Froge]

No. All the question asks is whether a current can flow across the circuit. That said, the five switches drawn in the circuit can be either closed or open. They are only shown as open to let you know that they are switches.

No one is correct so far.

[BAndrew]

No. All the question asks is whether a current can flow across the circuit. That said, the five switches drawn in the circuit can be either closed or open. They are only shown as open to let you know that they are switches.

What do you mean by "across"?

It can either go the upper way (that with the three switches) or the lower way (with the two switches). Or not?

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I think the five switches seen in the picture each simply have a probability of 1/3 to be open and 2/3 to be closed everytime you start the current. Closed switch means current can travel over it.

Well thank you that should be my mistake! So it will (probably) be 2/3 * 2/3 *2/3 + 2/3 * 2/3 - (2/3)^5 =
72/243 + 108/243 - 32/243 = 148/243 =~ 0,609 =~ 60,9%

[Froge]

^das correct

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So it will (probably) be 2/3 * 2/3 *2/3 + 2/3 * 2/3 - (2/3)^5 =

72/243 + 108/243 - 32/243 = 148/243 =~ 0,609 =~ 60,9%

Just so I can die in peace - what is it you're substracting there? The probability that all switches are closed I presume? In that case I'm relieved because it means I merely misunderstood the drawing instead of having forgotten everything I learned about math.
I thought the cables continued from the corner points to the respective poles, in which case it wouldn't matter if both lines are closed or only one.
(Which IS the only thing that would make sense since there's no power source specified... but anyway.)

[BAndrew]

^das correct

In English please.

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Just so I can die in peace - what is it you're substracting there? The probability that all switches are closed I presume? In that case I'm relieved because it means I merely misunderstood the drawing instead of having forgotten everything I learned about math.
I thought the cables continued from the corner points to the respective poles, in which case it wouldn't matter if both lines are closed or only one.
(Which IS the only thing that would make sense since there's no power source specified... but anyway.)

Yes.