Questions: Probability of independent events: Decimal answers A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d, c- and only one correct answer. What is the probability that she answered neither of the problems correctly?

Solution Steps

Each problem has 5 answer choices, and only one is correct. Therefore, the probability of answering a single problem incorrectly is: \[ P(\text{incorrect}) = \frac{4}{5} \]

Since the two problems are independent, the probability of answering both incorrectly is the product of the individual probabilities: \[ P(\text{both incorrect}) = P(\text{incorrect}) \times P(\text{incorrect}) = \frac{4}{5} \times \frac{4}{5} \]

Multiply the probabilities: \[ P(\text{both incorrect}) = \frac{4}{5} \times \frac{4}{5} = \frac{16}{25} \]

Final Answer