Question

A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of ten steps he is one step away from the starting point is

• A. \(\dfrac{2^5\cdot3^5}{5^{10}}\)
• B. \(462\left(\dfrac{6}{25}\right)^5\)
• C. \(231\cdot\dfrac{3^5}{5^{10}}\)
• D. none of these

Hint:

Check parity (odd/even) before lengthy probability calculations.

Answer 1

The Correct Option is D

Step 1: After 10 steps, distance from start must be odd.
Step 2: Net displacement after even number of steps is always even.
Step 3: Hence probability is zero.