A quiz consists of 10 multiple-choice questions. Each question has 5 possible answers and only one of them is correct. A student has not studied for the quiz and will pick his answers randomly.
1)Define the random variable x that will be used for problem, and give the probability of “success” p.
I know n=10 x= correct answer 0;1;2;...10
2)What is the probability that the student will get none of the correct answers?
3) If 60% is the lowest passing score, what is the probability that the student will get a passing score?
in one town 44% of all voters are democrats. if two voters are randomly selected for a survey, find the probability that they are both democrats. round to the nearest thousandth
1) In this problem, the random variable x represents the number of correct answers the student will get on the quiz. So, possible values for x can be any whole number from 0 to 10, since the student can get 0 to 10 answers correct.
The probability of success, denoted as p, is the probability that the student answers a question correctly. In this case, each question has 5 possible answers, and only one of them is correct. Therefore, the probability of selecting the correct answer by guessing randomly is 1 out of 5, or 1/5. So, p = 1/5.
2) To find the probability that the student will get none of the correct answers, we need to calculate the probability of x = 0, which means the student gets none of the answers correct.
The probability of getting x = 0 is calculated using the binomial probability formula. The formula is:
P(x) = nCx * (p^x) * ((1-p)^(n-x))
For x = 0, we have:
P(x=0) = 10C0 * (1/5)^0 * ((1 - 1/5)^(10-0))
Simplifying this expression, we have:
P(x=0) = 1 * 1 * (4/5)^10
Calculating this expression, P(x=0) is approximately equal to 0.1074. So, the probability that the student will get none of the correct answers is 0.1074 or approximately 10.74%.
3) To find the probability that the student will get a passing score, we need to calculate the probability of x being greater than or equal to the lowest passing score, which is 60%.
The probability of getting a passing score is the sum of the probabilities of x values greater than or equal to 6 (since 60% of 10 is 6).
P(x ≥ 6) = P(x=6) + P(x=7) + ... + P(x=10)
Using the binomial probability formula, we can calculate each individual probability and sum them up:
P(x ≥ 6) = 10C6 * (1/5)^6 * (4/5)^(10-6) + 10C7 * (1/5)^7 * (4/5)^(10-7) + ... + 10C10 * (1/5)^10 * (4/5)^(10-10)
Evaluating this expression, P(x ≥ 6) is approximately equal to 0.026.
Therefore, the probability that the student will get a passing score is approximately 0.026 or 2.6%.