How to Calculate the Probability of Getting 4 out of 5 Questions Correct on a True/False Quiz

You have a 5 question, true/false quiz.What is the probability that you choose each answer at random and get 4 of the questions correct?

To calculate the probability of getting 4 out of 5 questions correct on a true/false quiz by choosing answers at random, we need to determine the number of favorable outcomes and the total number of possible outcomes

To calculate the probability of getting 4 out of 5 questions correct on a true/false quiz by choosing answers at random, we need to determine the number of favorable outcomes and the total number of possible outcomes.

In this case, each question can be answered in one of two ways: true or false. Therefore, the total number of possible outcomes for all 5 questions is 2^5 = 32, because there are 2 options for each of the 5 questions.

Now, let’s calculate the number of favorable outcomes, i.e., the number of ways we can choose 4 correct answers out of 5 questions. We can use combinations to determine this. The formula for combinations is:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of items, and r is the number of items to be chosen.

In this case, we have 5 questions (n = 5) and we want to choose 4 questions correctly (r = 4). Plugging these values into the combination formula, we get:

C(5, 4) = 5! / (4! * (5-4)!)
= 5! / (4! * 1!)
= 5

So, there are 5 different ways to choose 4 correct answers out of 5 questions.

Therefore, the probability of getting exactly 4 questions correct is the ratio of the number of favorable outcomes to the total number of possible outcomes:

P(4 out of 5 correct) = Favorable outcomes / Total outcomes
= 5 / 32
= 0.15625
= 15.625%

Thus, the probability of randomly answering 4 questions correctly on the 5-question true/false quiz is approximately 15.625%.

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