Probability questions?

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Probability questions?

Two questions:

Find the probability of answering two multiple choice questions correctly if random guesses are made. Assume the questions each have five choices for the answer.
Only one of the choices is correct.

Find the probability of answering two true or false questions correctly if random guesses are made.
Only one of the choices is correct.

My issue: I don't know which probability rule to apply here...

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Answer 1 · 2017-07-11T20:04:33

First question:
You can reason the situation logically, or you can apply a law.

Probability of an event $= \frac{number of wanted outcomes}{total number of possible outcomes}$ $=("number of wanted outcomes")/("total number of possible outcomes")$

If there are $5$ $5$ possible answers for each question, there are:
$5 \times 5 = 25$ $5 xx5 =25$ possible combinations. Of these $25$ $25$ possibilities, there is only one combination of $2$ $2$ correct answers.
$P (2 correct answers) = \frac{1}{25}$ $P("2 correct answers") = 1/25$

Or you can use the law which says:

$P (2 correct answers)$ $P(2 "correct answers")$

$P (C, C) = P (first C) and P (second C)$ $P(C,C) = P("first "C) and P("second "C)$
"AND" implies multiply.

$= \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}$ $= 1/5 xx 1/5 = 1/25$

Second question:
The approach is the same, but there are only 2 options, each question is either "True or False"

$2 \times 2 = 4$ $2xx2 = 4$

Only one combination is correct. $\frac{1}{4}$ $1/4$

$P (C, C) = P (C) \times P (C) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ $P(C,C) = P(C) xx P(C) = 1/2 xx 1/2 = 1/4$

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