Toss 4 times Suppose you toss a fair coin 4 times. Let X=...

Toss 4 times Suppose you toss a fair coin 4 times. Let $X=$ the number of heads you get.
(a) Find the probability distribution of $X$.
(b) Make a histogram of the probability distribution. Describe what you see.
(c) Find $P(X \leq 3)$ and interpret the result.

Key Concepts

Cumulative Probability

Cumulative probability is the sum of the individual probabilities for outcomes up to a specified value. It is useful for determining the likelihood that the random variable falls within a certain range and for making probabilistic interpretations regarding events such as obtaining at most a given number of successes.

Histogram

A histogram is a graphical representation of the probability distribution of a discrete random variable. In this context, each bar represents the probability of obtaining a specific count of successes, allowing one to visualize the spread and symmetry (or skewness) of the distribution.

Probability Distribution

A probability distribution for a discrete random variable lists all possible outcomes of the experiment along with their associated probabilities. It provides a complete description of the likelihood of each outcome, allowing for further calculations and interpretations.

Binomial Distribution

A binomial distribution arises from a fixed number of independent trials with two possible outcomes (success and failure) where the probability of success is constant. It is used to model the number of successes in a series of experiments, such as the number of heads when tossing a coin multiple times.

Combinatorial Analysis

Combinatorial analysis involves counting the number of ways that a particular outcome can occur using combinations. This is crucial in problems like coin tossing where the number of ways to achieve a certain number of heads is determined by the binomial coefficient, often written as 'n choose k'.

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