Question

For each question on a multiple choice test, there are 5 possible answers, of which exactly one is correct. If a student selects answers at random, give the probability that the first question answer correctly is question 4.
Please, help. I don't know how to start but \(P(x_i)=\dfrac{1}{5}\)

Answer 1

If the first correct answer is question 4, then the first 3 trial is failed
so that P(1') =4/5
P(2') =4/5
P(3')=4/5
next is P(4) =1/5
then??

Answer 2

I think you need to multiply P(1'), P(2') P(3') P(4')

Answer 3

I know, but what I need is how to put it in logic. I can just give out the answer :)

Answer 4

So, the probability to get the 4th one is the first correct answer is
P(first failed + second failed+third failed + fourth win) =
\[P(1'\cap 2'\cap 3'\cap 4)=P(1')*P(2')*P(3')*P(4)=(\dfrac{4}{5})^3*\dfrac{1}{4}\]

Answer 5

Am I right?

Answer 6

Hm.

so he could do:

1) Answer first one, the probability is 1/5
2) Don't answer first one, answer second one, probability is 4/5*1/5
3) don't answer first one,don't answer second one, answer third one, probability is 4/5*4/5*1/5
4) Don't answer first one, dont answer the second one, don't answer the third one,answer the fourth one, probability is: 4/5*4/5*4/5*1/5

1) 1/5
2)4/20
3)16/125
4)64/625

Now all you need to do is sum up all the probabilities,I think

Answer 7

Thank you very much. I got you, just correct a little bit by replace "Don't answer" by " wrong answer" :)

Answer 8

sorry for my English, I am not a native speaker;) And you are welcome,I hope I am correct.. Maybe @waterineyes could check?

Answer 9

He he he he, you just scared me..!!

Answer 10

I got notification like : "Sorry for my english, I am not a native speaker.." and you tagged me..

I thought you found out, I don't know how, that my english is also very poor.. :)

Answer 11

haha,sorry about that! Your English seems to be alright;)

Answer 12

I have got rusty on these topics.. :(