A game show gives contestants 5 questions with 3 possible answers and awards $10 for every correct answer.If a contestant answers all 5 questions correctly,they win an extra $500.What is the probability of a contestant who guesses at every question will get at least 2 questions correct?
A)0.54
B)0.46
C)0.40
D)0.33

Question

Quizplus · Accepted Answer

The probability of guessing at least 2 questions correctly out of 5 can be calculated by finding the complement of the probability of guessing 0 or 1 question correctly. The probability of guessing a question correctly is 1/3, and incorrectly is 2/3. Using the binomial probability formula, we calculate the probabilities for 0 and 1 correct guesses and subtract from 1.For 0 correct guesses: $P(X=0) = \binom{5}{0} (1/3)^0 (2/3)^5 = (2/3)^5$For 1 correct guess: $P(X=1) = \binom{5}{1} (1/3)^1 (2/3)^4 = 5 * (1/3) * (2/3)^4$Adding these probabilities gives the probability of getting at most 1 question right. Subtracting this sum from 1 gives the probability of getting at least 2 questions right, which is approximately 0.54.

A Game Show Gives Contestants 5 Questions with 3 Possible