Answer:
Option: D is the correct answer.
D) 0.1563
Step-by-step explanation:
There are a total of 3 questions in a quiz.
We are asked to find the probability that at least two questions were correct.
Hence, we have to use binomial in order to find the probability.
We know that the probability of k success in n experiments is calculated by the formula:
\(P(X=k)=n_C_kp^kq^{n-k}\)
where p is the probability of success.
and q is the probability of failure.
Here p is the probability that the question is correct.
i.e. p=1/4
( Since out of the 4 choices 1 choice is correct)
Similarly,
q=3/4
( Since out of the 4 choices 3 are incorrect)
Hence, we are asked to find:
\(P(X\geq 2)\)
i.e. we have to find:
\(P(X=2)+P(X=3)\)
Here we have, n=3
\(P(X=2)+P(X=3)\\\\=3_C_2(\dfrac{1}{4})^2(\dfrac{3}{4})^1+3_C_3(\dfrac{1}{4})^3(\dfrac{3}{4})^0\\\\=\dfrac{9}{64}+\dfrac{1}{64}\\\\\\=\dfrac{10}{64}\\\\\\=0.15625\)
Hence, the probability is:
0.1563
