Thank you for the explanation MathMate! Would the answer to this question be A?

Darby guesses the answers to six questions on the math portion of her college entrance exam. Each question is a true or false question. What is the approximate probability that at least 4 of her answers are correct?

A. 0.23
B. 0.34
C. 0.66
D. 0.78

Sorry that the previous response was for 4 correct.

The number ways to have at least 4 correct is
(6,4)+(6,5)+(6,6)
=15+6+1
=22
To total number of ways to respond is
2^6=64
So the probability is 22/64.

What is the probability that at least one of the three people has alzheimer's diseas

To find the approximate probability that at least 4 of Darby's answers are correct, we need to calculate the probability of 4, 5, and 6 correct answers separately, and then add them together.

First, let's calculate the probability of getting exactly 4 correct answers.

The probability of getting a single question correct is 1/2, since each question is a true or false question. The probability of getting a single question wrong is also 1/2.

The number of ways to choose 4 questions out of 6 is given by the binomial coefficient (6 choose 4), which can be calculated as: 6! / (4! * (6-4)!) = 6! / (4! * 2!) = (6 * 5 * 4 * 3) / (4 * 3 * 2 * 1) = 15.

The probability of getting exactly 4 correct answers is then: (1/2)^4 * (1/2)^(6-4) = (1/2)^4 * (1/2)^2 = 1/16.

Next, let's calculate the probability of getting exactly 5 correct answers.

Similarly, the probability of getting exactly 5 questions correct is: (1/2)^5 * (1/2)^(6-5) = 1/32.

Lastly, let's calculate the probability of getting all 6 correct answers.

The probability of getting all 6 questions correct is: (1/2)^6 = 1/64.

Now, let's add up the probabilities of these three cases: 1/16 + 1/32 + 1/64 = 3/64.

The approximate probability that at least 4 of Darby's answers are correct is approximately 3/64.

By comparing this result to the answer choices, we see that none of the given answer choices match. Therefore, none of the answer choices A, B, C, or D would be the correct answer.

Please note that the calculation above assumes that each question is an independent event, and the probability of guessing correctly is the same for each question.