Probability question

[dmini]

Same as TimberWolf here as well

I mean the 4/9 version

[TimberWolf]

Okay, here's another way of thinking about it.

He can only get one right in total by either getting the first one right (1 in 3 chance) and the second one wrong (2 in 3) or ditto but reversed.

So the probabilty of getting just one right is 1/3 * 2/3 + 2/3*1/3 = 4/9

Just to explain that a bit more with an example, assume the correct answers are True and True.

Out of the 9 possible answer combinations, the subject could choose only TF, TI, FT, IT to get one right (TT is disallowed since he'd then get both right) and the remaining combinations don't have a T in them.

The 1 in 9 probability I gave first was the probability of getting both right. Oops, it's been a while, more haste less speed, was washing the dogs hair, etc.

[Pinto]

Went for:

P(Either one right) = 1 - ((Both Wrong 4/9) + (Both right 1/9))

[DS23]

the student will inevitably flunk.

[aussielong]

The actual answer is 4/9. But I can't work out why.
Your sample space is of course correct.

i think its something like

P(getting exactly 1 right) = 1- P(getting none or two right)
= 1 - P(none right) - P(two right) = 1 - (2/3*2/3) - (1/3*1/3)
= 1 - 4/9 - 1/9
= 9/9 - 4/9 - 1/9
= 4/9

[IR35 Avoider]

I thought it was going to be a trick question - was pleased that I got it right.

My thought process was:-

There are 3x3=9 possible combinations of answers to the two questions

To satisfy the conditions, one must get the 1 right answer to the first question and one of 2 wrong answers to the second, i.e 1x2 ways if the first question is correct. Similarly, there are 2x1 ways to satisfy the condition if the answer to the first question is wrong. So there are 1x2+2x1 ways to get one correct answer. So the probability is 4/9.

[Xenophon]

Everyone who has made a serious post in this thread is awarded +5 Xeno Geek Points.

sasguru is awarded another +5 Xeno Geek Points as the thread starter.

[Diver]

Probability of this becoming the most boring thread in CUK history = ?

Please write your answers on the back of a £20 note and post them to Sasguru

[sasguru]

Probability of this becoming the most boring thread in CUK history = ?

Please write your answers on the back of a £20 note and post them to Sasguru

Thought you weren't coming back? Not my fault it all goes over your head

[TimberWolf]

An interesting thing here is when you start playing with the algebra of the solutions. For example:

Take w as the probability of a wrong answer = 2/3, and r the probability of a right answer. Then taking one of the solutions : wr + rw, simplifies to 2rw = 2*1/3*2/3 = 4/9. All fine and dandy, but's what's the intuitive reasoning behind 2rw? i.e. how do you get straight to 2rw by thought alone?

Likewise if you take one of the other solutions, it simplifies to 1 - (w+r)^2 -2wr. If you equate this with 2wr you find w+r=1. Other interesting results coming from manipulating the algebra thusly is left as an exercise of the reader.

For instance you could start with the knowledge the r=1-w and see where that gets you, but now I'm doing all the work for you.