Probability Explanation And Exercises Worksheet Page 19
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37Binomial Distribution
by David M. Lane
Prerequisites
• Chapter 1: Distributions
• Chapter 3: Variability
• Chapter 5: Basic Probability
Learning Objectives
1. Define binomial outcomes
2. Compute the probability of getting X successes in N trials
3. Compute cumulative binomial probabilities
4. Find the mean and standard deviation of a binomial distribution
When you flip a coin, there are two possible outcomes: heads and tails. Each
outcome has a fixed probability, the same from trial to trial. In the case of coins,
heads and tails each have the same probability of 1/2. More generally, there are
situations in which the coin is biased, so that heads and tails have different
probabilities. In the present section, we consider probability distributions for which
there are just two possible outcomes with fixed probabilities summing to one.
These distributions are called binomial distributions.
A Simple Example
The four possible outcomes that could occur if you flipped a coin twice are listed
below in Table 1. Note that the four outcomes are equally likely: each has
probability 1/4. To see this, note that the tosses of the coin are independent (neither
affects the other). Hence, the probability of a head on Flip 1 and a head on Flip 2 is
the product of P(H) and P(H), which is 1/2 x 1/2 = 1/4. The same calculation
applies to the probability of a head on Flip 1 and a tail on Flip 2. Each is 1/2 x 1/2
= 1/4.
Table 1. Four Possible Outcomes.
Outcome
First Flip
Second Flip
1
Heads
Heads
2
Heads
Tails
203
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