a 10 question multiple choice test has 4 possible answer for each question. A student selects at least 6 correct answers.

Find probability of this event:

(multiple choice)
A) .118
B) .995
C) .068
D) .571

he got 6 right, 4 wrong. The question has no answer. Did he randomly guess, or did he know the answers to only six?

If he knew the answers to six, the probability is 1 that he gets those six.
If he knows 5, the prob is 1 he gets those right, plus pr =4(1/4)(3/4) he gets one more or a pr of .75 he gets six right knowing 5, guessing on the last four.

Well, we need to know how many he knew, I think.

To find the probability of a student selecting at least 6 correct answers on a 10-question multiple-choice test with 4 possible answers for each question, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = (n C k) * p^k * (1 - p)^(n - k)

where:
- P(X = k) is the probability of getting exactly k successes,
- n is the number of trials or questions (10 in this case),
- k is the number of successful outcomes (correct answers in this case),
- p is the probability of success on a single trial (probability of selecting the correct answer, which is 1/4),
- (n C k) is the number of combinations of n items taken k at a time.

To find the probability of getting at least 6 correct answers, we need to calculate the sum of the probabilities of getting exactly 6, 7, 8, 9, and 10 correct answers on the test:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

Let's calculate each individual probability:

P(X = 6) = (10 C 6) * (1/4)^6 * (3/4)^(10 - 6)
P(X = 7) = (10 C 7) * (1/4)^7 * (3/4)^(10 - 7)
P(X = 8) = (10 C 8) * (1/4)^8 * (3/4)^(10 - 8)
P(X = 9) = (10 C 9) * (1/4)^9 * (3/4)^(10 - 9)
P(X = 10) = (10 C 10) * (1/4)^10 * (3/4)^(10 - 10)

Now we can add these probabilities together to find the probability of getting at least 6 correct answers:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

After calculating the values for each individual probability and summing them up, we find that the correct answer is not provided in the options A, B, C, or D.