A toy train can produce one of two musical sounds with equal probability on each trial. What is the probability that the same sound would be produced five times in a row?

• A. 1/32
• B. 11/32
• C. 1/16
• D. 11/16

Answer: (A)

This question tests understanding of independent trials with two equally likely outcomes and counting all favorable patterns. Each trial has two sounds, each with probability 1/2, and we want the same sound five times in a row. There are two favorable patterns: all five sounds are the first type, or all five are the second type. Each specific five-in-a-row pattern has probability (1/2)^5 = 1/32, so together they total 2 × 1/32 = 1/16. A quick alternative view: fix the first sound, then the next four must match it, giving (1/2)^4 = 1/16. The given option 1/32 would be the chance of five repeats of a particular sound, not of either sound.