Find the probability of correctly answering the first 4 questions on a multiple choice test if random guesses are made and each question has 3 possible answers.
A) 4/3 B) 1/81 C)1/64 D)3/4
I automatically think D.
1/3 * 1/3 * 1/3 * 1/3 = 1/81
thanks
To solve this problem, we need to consider the probability of correctly guessing the answer for each question and combine these probabilities for all four questions.
Since there are 3 possible answers for each question and we are making random guesses, the probability of guessing the correct answer for a single question is 1/3.
To find the probability of guessing correctly for all four questions, we multiply the probabilities together:
P(correct answer for question 1 and question 2 and question 3 and question 4) = (1/3) * (1/3) * (1/3) * (1/3)
Rearranging the equation:
P(correct answer for all four questions) = (1/3)^4
Simplifying:
P(correct answer for all four questions) = 1/81
Therefore, the correct answer is B) 1/81.
To find the probability of correctly answering the first 4 questions on a multiple choice test by making random guesses, you need to consider the number of possible outcomes.
For each question, there are 3 possible answers. Therefore, the total number of possible outcomes for all 4 questions is 3 * 3 * 3 * 3 = 81.
Now, if you make random guesses, there is only 1 correct answer for each question. Since there are 4 questions, the number of successful outcomes (i.e., getting all 4 answers correct) is only 1.
The probability of an event happening is defined as the number of successful outcomes divided by the number of possible outcomes. So, in this case, the probability is 1/81.
Therefore, the correct answer is B) 1/81.