A 10-question multiple choice test has 4 possible answers
for each question. A student guesses on all ten answer.
a)What is the probability that the student selects at least 6 correct answers?
b)Is getting exactly 10 questions correct the same probability as getting exactly zero correct?
c)Describe the steps needed to calculate the probability of getting at least six questions correct if the student randomly guesses. You do not need to calculate this probability.
Pleaaaasssee heeelppp I am super stuck and don't know how to answer this question!!!!!
4/4096
I understand that you are having trouble with probability calculations. Let me help you step-by-step.
a) To find the probability that the student selects at least 6 correct answers, we can use the binomial probability formula. The formula is as follows:
P(x = k) = nCk * p^k * q^(n-k)
Where:
- n is the total number of trials (number of questions)
- k is the number of successful outcomes (number of correct answers)
- nCk is the combination formula, also known as "n choose k"
- p is the probability of success (probability of selecting the correct answer on a single question)
- q is the probability of failure (probability of selecting the incorrect answer on a single question), which is equal to 1 - p.
In this case, n = 10 (since there are 10 questions) and p = 1/4 (since there are 4 possible answers for each question and the student is guessing).
To find the probability of at least 6 correct answers, you would sum the probabilities of getting exactly 6, 7, 8, 9, and 10 correct answers. You can calculate each individual probability using the formula mentioned above and then add them together.
b) No, getting exactly 10 questions correct is not the same probability as getting exactly zero correct. The probability of getting exactly zero correct would be the same as getting all the questions wrong, which would be (3/4)^10, since there are 3 incorrect answers for every question.
c) To calculate the probability of getting at least six questions correct, you would compute the individual probabilities of getting exactly 6, 7, 8, 9, and 10 correct answers, using the binomial probability formula mentioned earlier. Then, you would sum these individual probabilities together to find the overall probability. This can be done using a calculator or by breaking it down into smaller steps.
I hope this explanation helps you understand how to approach this problem. If you have any further questions, feel free to ask.
No worries, I'll be happy to help you with this problem step by step!
a) To find the probability that the student selects at least 6 correct answers, we need to consider two scenarios: the student selects exactly 6 correct answers, and the student selects 7, 8, 9, or all 10 correct answers.
1. Probability of selecting exactly 6 correct answers:
The probability of getting a single question correct by random guessing is 1/4. Therefore, the probability of getting exactly 6 correct answers is (1/4)^6 because the student needs to get all 6 answers correct, and (3/4)^(10-6) because the student also needs to get the remaining 4 answers wrong. Multiplying these probabilities gives you the probability of selecting exactly 6 correct answers.
2. Probability of selecting 7, 8, 9, or all 10 correct answers:
You can calculate the probability of each of these scenarios using the same logic as in step 1. For example, to find the probability of selecting exactly 7 correct answers, you would multiply (1/4)^7 and (3/4)^(10-7).
Finally, to get the probability that the student selects at least 6 correct answers, you need to add up the probabilities from step 1 and step 2.
b) The probability of getting exactly 10 questions correct is not the same as getting exactly zero correct. When the student guesses randomly, the probability of getting a single question correct is 1/4, and the probability of getting a single question wrong is 3/4. Therefore, if the student guesses on all 10 questions, the probability of getting exactly 10 correct is (1/4)^10. On the other hand, getting exactly zero correct is (3/4)^10. As you can see, these probabilities are different.
c) To calculate the probability of getting at least six questions correct if the student randomly guesses, you would follow these steps:
1. Determine the probability of getting exactly 6 correct answers using the method described in step a) above.
2. Determine the probability of getting exactly 7, 8, 9, or all 10 correct answers using the same method.
3. Add up the probabilities calculated in steps 1 and 2 to find the probability of getting at least six questions correct.
Remember, you don't need to perform these calculations unless you're specifically asked to in the question. I hope this helps you understand the problem better! Let me know if you have any further questions.
How does a differ from c?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
b) (3/4)^20
c) "at least 6" translates to either 6, 7, 8, 9 or 10.
Either-or probabilities are found by adding the individual probabilities.
P(correct) = 1/4
P(incorrect) = 3/4
p(6 correct) = (1/4)^6 * (3/4)^4
Calculate for 7, 8, 9, and 10, then add.