find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has six possible answers

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1/6 * 1/6

To find the probability of correctly answering the first 2 questions on a multiple choice test when random guesses are made, we need to consider the number of possible outcomes and the number of favorable outcomes.

In this case, each question has six possible answers. Since the questions are multiple-choice, we can assume that one of the six options is correct for each question. Therefore, the number of favorable outcomes (the number of correct answers) for each question is only 1.

Now, let's calculate the total number of possible outcomes for each question. Since there are six possible answers for each question, the total number of possible outcomes is also 6.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes. Since there is only 1 favorable outcome (correct answer) for each question, and a total of 6 possible outcomes (the 6 answer choices), the probability of correctly answering each question is:

P(correct answer) = Number of favorable outcomes / Total number of possible outcomes
= 1 / 6

To find the probability of correctly answering both questions, we need to find the probability of both events happening at the same time. To calculate this, we multiply the probabilities of each event (since the events are independent):

P(both questions correct) = P(correct answer for question 1) * P(correct answer for question 2)

P(both questions correct) = (1 / 6) * (1 / 6)
= 1 / 36

Therefore, the probability of correctly answering the first two questions on the multiple-choice test if random guesses are made is 1/36.