A student takes a quiz consisting of 5 multiple choice questions. Each question has 4 possible answers. If a student is guessing the answer at random and answer to different are independent, then the probability of atleast one correct answer is
Step-by-step Solution:
The probability of a correct answer: \[ p = \frac{1}{4} = 0.25 \] The probability of a wrong answer: \[ q = \frac{3}{4} = 0.75 \] Total questions: \[ n = 5 \] Probability of at least one correct answer (\(x \geq 1\)): \[ P(x \geq 1) = 1 - P(x = 0) \] \[ P(x \geq 1) = 1 - \binom{5}{0} p^0 q^5 \] \[ P(x \geq 1) = 1 - (0.75)^5 \] \[ P(x \geq 1) = 1 - 0.2373 \] \[ \Rightarrow \mathbf{P(x \geq 1) \approx 0.7627} \]