landen has forgotten to study for his weekly ...
landen has forgotten to study for his weekly ap chemistry quiz. he knows there will be 5 multiple - choice problems with only 3 possible choices, of which 1 is correct. if he randomly guesses for each question, what is the probability that he will get a 100% on the quiz? a $\frac{5}{3}$ b $\frac{1}{3}$ c $\frac{32}{243}$ d $\frac{1}{243}$
Answer
# Answer:
D. $\frac{1}{243}$
# Explanation:
## Step1: Probability of one - question correct
The probability of getting a single multiple - choice question correct when there are 3 choices and 1 correct answer is $\frac{1}{3}$.
## Step2: Probability of all 5 questions correct
Since the questions are independent events, the probability of getting all 5 questions correct is the product of the probabilities of getting each question correct. Using the multiplication rule for independent events $P(A\cap B\cap C\cap D\cap E)=P(A)\times P(B)\times P(C)\times P(D)\times P(E)$. Here, $P(A) = P(B)=P(C)=P(D)=P(E)=\frac{1}{3}$. So the probability is $\left(\frac{1}{3}\right)^5=\frac{1}{243}$.