Random Walks and Certainty?

📌 CONCEPT: The probability of reaching a destination in a random walk is determined by the number of choices at each step and the number of steps required to reach the goal.

📐 RULE / FORMULA: The probability of reaching the goal in exactly 'n' steps is given by the formula 1 - (probability of not reaching the goal in 'n' steps)^(total number of steps).

💡 WORKED EXAMPLE: If Sara has 5 roads to choose from at each intersection, and she wants to be at the coffee shop within 5 steps, the probability of reaching the coffee shop in exactly 3 steps is (1 - (4/5)^3)^5 = 0.0320 or 3.2%.

⚠️ COMMON MISTAKE: Students often forget to calculate the probability of not reaching the goal in 'n' steps, which leads to incorrect results.