basic algebra

Question

A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had
5

answer choices –
a

,
b

,
c

,
d

,
e

– and only one correct answer. What is the probability that she answered neither of the problems correctly?

Answer 1

Probability is defined as: (number of successful outcomes) / (number of possible outcomes).

 

The words "neither of the problems correctly" may be interpreted to mean that both of the questions had a wrong answer.

 

The 25 possible outcomes (for answer choices) are:

   aa ab ac ad ae ba bb bc bd be ca cb cc cd ce da db dc dd de ea eb ec ed ee

 

Suppose, for example, that the key for the two questions was bc and the choice of key values was uniformly random, the 16 successful outcomes would be:

   aa ab   ad ae    ca cb  cd ce da db  dd de ea eb  ed ee

 

So, Kenneth's answer of 16/25 is correct.

Answer 2

If she only has a 2 in 10 chance in getting it correct, since there are only two correct answers in total for the questions and 10 choices to choose from in total.  So she would have a 4 in 5 chance of getting it incorrectly.

Answer 3

P(incorrect answer) =4/5

 

P(both incorrect) = (4/5)² =16/25