Question

each question of a 5-question m multiple choice test has 5 possible answers. suppose a student picks an answer at random for each question. Find the probability the student selects the correct answer on all the questions. the probability that all the answers are correct is ______. (type an integer or simplified fraction).

Answer 1

`P(all-correct)=(1)/(3125)`

Step-by-step explanation

We want to find the probability that the student selects the correct answer on all questions.

For each question, there is only 1 possible correct answer out of 5 options. This means that for each question, the probability of selecting the correct answer is:

`P(\text{correct)}=(1)/(5)`

Therefore, for 5 questions (with 5 options each), the probability of selecting the right answer will be the product of selecting the right answer for each of the 5 questions.

That is:

`\begin{gathered} P(all-correct)=(1)/(5)\cdot(1)/(5)\cdot(1)/(5)\cdot(1)/(5)\cdot(1)/(5) \\ P(all-correct)=(1)/(3125) \end{gathered}`

That is the answer.