On an eight question true-false quiz, a student guesses each answer. What is the probability that he/she gets at least one of the answers correct?

Step-by-step explanation:

Given

Required

Probability that s/he gets at least one correctly

First, we calculate the probability of answering a question correctly

Since, there are just 2 choices (true or false), the probability is:

Similarly, the probability of answering a question, wrongly is:

The following relationship exists, in probability:

So, to calculate the required probability.

First, we calculate the probability that he answers none of the 8 questions correctly.

Substitute in

Take LCM

Hence, the probability that s/he gets at least one correctly is 0.9961

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)