On a nine-question true-or-false test you randomly guess at the answers. What is the probability that you get all nine answers correct? What is the probability that you get all nine answers wrong?
since the questions are (presumed to be) independent, the probability in both cases is just (1/2)^9 = 1/512
To solve this problem, we need to understand the concept of probability.
The probability of getting a single question correct is 1/2, as there are only two possible outcomes: true or false, and you are guessing randomly. Similarly, the probability of getting a single question wrong is also 1/2.
To find the probability of getting all nine answers correct, we need to multiply the probability of getting a single question correct by itself nine times:
P(All correct) = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = (1/512) ≈ 0.001953125
So, the probability of getting all nine answers correct is approximately 0.001953125 or 0.1953%.
On the other hand, to find the probability of getting all nine answers wrong, we need to multiply the probability of getting a single question wrong by itself nine times:
P(All wrong) = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = (1/512) ≈ 0.001953125
So, the probability of getting all nine answers wrong is also approximately 0.001953125 or 0.1953%.