Quiz has 6 questions. Each question has five possible answers,
only one of each 5 answers is correct.
If student randomly guesses on all six questions,
what is the probability to answer 2 questions right?
Tip: first, you have to define parameters of Binomial distribution:
n - how many trials/questions do you have
p - probability guessing right answer to each question
x - how many successes do you expect.
Then use Appendix Table or Excel function for Binomial distribution.
Answer
Assuming the 6 questions are independent,
n=6 (questions)
p=probability of guessing the right answer (1/5)
x=exactly the number of successes over the 6 questions (2).
Look up the appendix table, or the Excel function to calculate the probability.
Alternatively, use the formula:
P(x) = C(n,x)*px*(1-p)n-x
Where C(n,x) represents the number of combinations of taking n things, x at a time.
on a test midterm exam each multiple choice question provides five possible answers. what is the probability of randomly guessing three consecutive questions correctly?
.24576
You're welcome
0.24576
answer 0.24576
p(x=4)=0.24576
p(x=4) = binompdf(6, 1/5, 4) = 0.2458
Good
To calculate the probability of answering 2 questions right out of 6, we can use the binomial distribution formula:
P(x) = (nCx) * (p^x) * ((1-p)^(n-x))
Where:
- P(x) is the probability of getting exactly x successes
- n is the number of trials/questions (which is 6 in this case)
- p is the probability of guessing the right answer for each question (which is 1/5 or 0.2 in this case)
- x is the number of successes we want (which is 2 in this case)
Using this formula, we can calculate the probability as follows:
P(2) = (6C2) * (0.2^2) * (0.8^(6-2))
Let's break it down step by step:
1. Calculate the number of combinations: (6C2) = 6! / (2! * (6-2)!) = 15
2. Raise the probability of guessing right (0.2) to the power of the number of successes we want (2): (0.2^2) = 0.04
3. Raise the probability of guessing wrong (0.8) to the power of the number of failures (6-2): (0.8^4) = 0.4096
4. Multiply all the values together: P(2) = 15 * 0.04 * 0.4096 = 0.24576
Therefore, the probability of answering 2 questions right out of 6, when guessing randomly, is approximately 0.24576 or 24.576%.