Sally is completely unprepared for a three-question multiple-choice pop quiz, so she randomly guesses the answer to each question. if each question has four choices, then what is the probability that she gets at least two questions correct?
a) 0.0469
b) 0.0625
c) 0.1406
d) 0.1563

Option: D is the correct answer.

D) 0.1563

There are a total of 3 questions in a quiz.

We are asked to find the probability that at least two questions were correct.

Hence, we have to use binomial in order to find the probability.

We know that the probability of k success in n experiments is calculated by the formula:

where p is the probability of success.

and q is the probability of failure.

Here p is the probability that the question is correct.

i.e. p=1/4

( Since out of the 4 choices 1 choice is correct)

Similarly,

q=3/4

( Since out of the 4 choices 3 are incorrect)

Hence, we are asked to find:

i.e. we have to find:

Here we have, n=3

            Hence, the probability is:

                      0.1563

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.