Question

Given the quiz below, find the probabilities that follow. Round answers to four decimal places. 1, А В С 2, A B C 3. ABC 4. A B C 5. A B C Find the probability of getting 2 questions right.

Answer 1

When randomly guessing a question,

The probability of getting the answer correct $= \frac{1}{3}$

Let X denotes the number of right answers out of 5 questions in the quiz.

X ~ Binomial(5, 1/3)

The probability mass function of X is

z)=( ) * (1)! * (1--)5-*, x = 0, 1.2, 3, 4, 5

Now,

a) The probability of getting 2 questions right

$= P(X=2) = \binom{5}{2}*(\frac{1}{3})^{2}*(1-\frac{1}{3})^{5-2} = 0.329216$

b) The probability of getting 1 question wrong

= P( getting 4 questions right)

$= P(X=4) = \binom{5}{4}*(\frac{1}{3})^{4}*(1-\frac{1}{3})^{5-4} = 0.0411508$