multiple choice question has 5 available options, only 1 of which is correct. Students are allowed 2 attempts at the answer. A student who does not know the answer decides to guess at random, as follows:
On the first attempt, he guesses at random among the 5 options. If his guess is right, he stops. If his guess is wrong, then on the second attempt he guesses at random from among the 4 remaining options.
1. Find the chance that the student has to make two attempts and gets the right answer the second time.
2. Find the chance that the student gets the right answer.

Question

multiple choice question has 5 available options, only 1 of which is correct. Students are allowed 2 attempts at the answer. A student who does not know the answer decides to guess at random, as follows:
On the first attempt, he guesses at random among the 5 options. If his guess is right, he stops. If his guess is wrong, then on the second attempt he guesses at random from among the 4 remaining options. 
1. Find the chance that the student has to make two attempts and gets the right answer the second time.
2. Find the chance that the student gets the right answer.

amistre64 · Answer

assuming that the options are all equally confounding ....

the only possible ways to choose is:

wwwwr
wwwrw
wwrww
wrwww
rwwww

such that the first guess is .2, second guess is .25, third guess is .333, forth guess is .5, and fifth guess is 1

but i might be seeing that incorrectly :/

anonymous · Answer

1. P(right on second try)=P(wrong on 1 of 5)*P(right on 1 of 4)
=(4/5)*(1/4)

2. P(right answer)=1-P(wrong answer)
=1-P(getting first try wrong and getting second try wrong)
=1-(4/5)*(3/4)