Quiz has 6 questions. Each question has five possible answers,

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)*p^x*(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?

.324

.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%.