To determine the probability that Judy answers all questions correctly by guessing, we first need to examine the structure of the test. Each question has 4 possible answers, with only 1 being correct.
The probability of Judy guessing the correct answer for a single question is:
P(correct) = 1/4
Since the questions are independent, we can find the probability of Judy guessing all 10 questions correctly by multiplying the probabilities of guessing correctly for each individual question:
P(all correct) = P(correct) × P(correct) × … (10 times) = (1/4) ^ 10
Calculating this gives us:
P(all correct) = (1/4) ^ 10 = 1/1048576
This means that the probability of Judy guessing on all questions correctly is 1 in 1,048,576.
In conclusion, if Judy guesses on all questions, her chances of getting all of them right is extremely low, highlighting the importance of studying and preparing for tests.