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

Binomial Distribution — Preparation

This question tests your understanding of Binomial Distribution, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.

The binomial distribution models the number of successes in a fixed number of independent trials, where each trial has only two outcomes (success or failure) and the probability of success p stays the same. Examples include the number of heads in ten coin tosses or the number of defective items in a sample. The probability of exactly r successes in n trials is P(X = r) = nCr p^r q^(n-r), where q = 1 - p. The mean is np and the variance is npq. Exam questions test finding the probability of exactly, at least or at most r successes, and finding n, p or q when the mean and variance are given. For "at least one" questions, use the complement: P(X >= 1) = 1 - q^n. Since the mean np is always greater than the variance npq, an option that gives a variance larger than the mean can be ruled out straight away. Practise the binomial distribution questions below, each with a step-by-step solution.