Question

Krista has a quiz today. There are 4 questions with 4 options. Each question only has one correct answer. She wants to guess and get 3 out of the 4 questions right. What is the probability of her getting 3 right​

Answer 1

Answer: 4.68%

Step-by-step explanation: To calculate the probability of Krista getting 3 out of 4 questions right, we can use the binomial probability formula:

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

where:

- P(X = k) is the probability of getting exactly k questions right

- n is the total number of questions (4 in this case)

- k is the number of questions Krista wants to get right (3 in this case)

- p is the probability of getting one question right, which is 1/4 since there are 4 options for each question

Plugging in the values, we get:

P(X = 3) = (4 choose 3) * (1/4)^3 * (3/4)^1

P(X = 3) = 4 * 1/64 * 3/4

P(X = 3) = 0.046875

Therefore, the probability of Krista getting exactly 3 out of 4 questions right if she guesses randomly is 4.68%.

Answer 2

The probability is 0.258

Explanation:

In this question, we want to know the probability of Krista getting exactly 3 out of the options she chooses right.

For all the questions, there are 4 questions with 4 options each

Total number of options is 4 * 4 = 16 options

there are 3 wrong options and one correct option per question. Total number of correct option is 4 and the total number of wrong options is 12

Probability of selecting a wrong option is 12/16 = 3/4 while the probability of selecting a correct option is 1/4

Thus, we can use a Bernoulli approximation to get this probability of getting three right.

let the probability of selecting a correct option be p and that of a wrong option be a.

Probability of selecting exactly three correct ones will be;

P(r = 3) = nCr p^r q^(n-r)

where n is the total number of options and r is the number of options we are selecting to be correct.

The probability = 12C3 * (1/4)^3 * (3/4)^9

= 220 * 0.015625 * 0.075084686279 = 0.258