Some puzzles

The key word in the question for me is runway. And the answer is yes.

 

Swap
Yes
2nd set
Worried

 

Phoenix nights?

 

The plane wouldn't be stationary as the engines don't drive the wheels. The only effect the treadmill would have is slight resistance due to the bearings in the wheels

 

If the treadmill was moving exactly, the plane wouldn’t actually be ‘moving’ though would it? The wheels would be turning but no air would be passing over the plane, as it’s stationary in relation to the ground

 

The plane would be moving. The jets push the plane through the air. They don't drive the wheels

 

I know that, but it requires air movement over the wings to get it into the air. Until then it’s pushing it forward on the ground, against the wheels.

I could be wrong

 

Yes it needs air movement. I think where people get confused is assuming that the plane will stand still on the treadmill, it won't because the thrust will push it forwards through the air. The only thing the treadmill does is cause the wheels to spin at double the speed but the plane will move forwards and lift

 

You’re correct, of course. I’m not sure what I was thinking...

 

Switch, as you might have selected one with a goat and therefore the game show host has to pick the one with the other goat.

Doesn’t take off as air isn’t moving.

Don’t think it makes any difference. You know there is at least one in both of them.

There’s a 1/1000 chance you have it. The test tells you you don’t, but there’s 1/100 chance it’s wrong. Therefore I think the likelihood is 1/100000.

 

It's because logic tells you that it would work the same as a car on a rolling road or a human on a treadmill but the important thing to remember is a cars engine is connected to it's wheels and a humans heart is connected to it's legs. A planes engines are completely disconnected from the wheels so it would still move forwards. Easiest comparison I can think of is if you run on a treadmill you'll stay still but I could walk up behind you and shove you in the back and you'll go forwards. That's the jet engine thrusting.

I suppose if I'd worded it like that a lot earlier it would have been simpler

 

Honestly I’m embarrassed it took me so long for it to click, given that my job is entirely logic based.

I’m going to bed. That’s my excuse and I’m sticking to it, I was tired.

 

1. Swap, 1 in 3 chance if you don't, 2 in 3 if you do.
2. Assuming treadmill speed matches that of forward thrust of plane then no.
3. Set 1 as there are more permutations to getting 2 aces. In set 2 there are only 7 permutations to give you 2 or more aces as one of them has to be the ace of spades. In set 1 it's 16.
4. Not hugely. If you tested 10,000 people you'd get 100 positive results. Only 1 of those people would have the virus

 

Seems #2 is actually yes.

 

1 Always switch, see The Monty Hall problem for an explanation. Don't worry if you don't get it, it's the most counterintuitive phenomenon I know. Sometimes I understand it perfectly and can write it out, a week later my brain won't have it. I've wasted years of my life on this. Just know you should and the explanation doesn't really matter.

2 The theoretical answer to this is not actually the right answer. The theoretical answer is that as an aeroplane does not produce forward momentum via drive from the wheels, like a car for instance, but thrust from props or a jet engine, then the treadmill would have no influence and the plane would simply zip down the runway and take off. The reality is that we have friction, we have bearings in wheels that are not tested at speeds that the wheels would be required to spin for the plane to reach take-off speed and there'd be a catastrophic malfunction.

3 I can't work out the maths for this but as the second set gives limitations, the answer is the first. The second set is the Ace of spades in conjunction with other aces. The first set is any ace in conjunction with any other aces which gives you more permutations and the more possibilities the more chance of winning so it's the better bet.

4 If you test 100 people you'll get 1 false positive. If you test 1,000 you'll get 10 false positives. If you test 10,000 you'll get 100 false positives. As only 1 in 10,000 actually has the virus the chances of you having it even after a positive test is just 1%.

 

Arrgghhh!! Apologies ..... you are asolutely right!! (assuming the tyres and undercarriage can cope with double normal take off speed before the plane lifts and they dont burst/collapse causing the thing to slew off the conveyor and end up crashing in a ball of flame!) Bit like me trying to walk up a long down escalator without having a coronary 'episode'

 

Oops! Sorry Jay re number 2 I just posted something similar re tyres & undercarriage before I saew your (more serious answer. I know they test aircraft to destruction but given rotation speed of a large jet is something like 160 knots even with a headwind I think it is unlikely they test them to 320 knots I think the tyres would simply explode before the bearings failed!!.

 

What’s 170 as a percentage of 7711?

 

Ho! Jolly ho!!

Well we all make mistakes said the Dalek as he climbed off the dustbin (the old ones are the best!!) Just mine come in threes!

 

In Q 1 the Pr of getting the prize first guess is 1/3 = 0.333rec if you swap the Pr of getting the prize is .6666rec multiplied by 0.5 = 0.3333 so the probability is the same so the ANSWER IS IT DOES NOT MAKE ANY DIFFERENCE THE ODDS ARE THE SAME