Central Bucks School District
Ch. 17: Binomials
Example: Computer chips have a 25% chance of being defective. Create the probability distribution for X, if X is the # of defective chips in a sample of 3. What is the probability of having 2 or more defective chips?
|X |0 |1 |2 |3 |
|P(X) | | | | |
a) What is the probability of having 2 or more defective chips?
b) What is the probability of having 1 or less defective chips?
c) What is the probability of having exactly 2 defective chips?
BINOMIAL MODELS:
• Interested in the number of successes in a set number of trials
• 4 conditions that must apply:
o Only 2 possible outcomes (success/failure)
o Probability of success remains constant (called p)
o Number of trials is set/known (called n)
o Independent trials
▪ 10% Condition: If we cannot assume independence, we can proceed as long as the sample is smaller than 10% of the population
• If these 4 conditions apply, we have a Bernoulli trial
Notation:
µX= σX=
Example: It is known that only 15% of the population is left handed. Create a probability distribution for the number of left handed people in a sample of 3.
|X |P(X) |
|0 | |
|1 | |
|2 | |
|3 | |
Quicker way to get probabilities:
Formula: P(X = k) =
|X |P(X) |
|0 | |
|1 | |
|2 | |
|3 | |
Example: I am playing a game in which I have a 39% chance of winning each time I play. Create the probability distribution for the number of wins out of 5 plays of the game.
STEP 1: Check if the problem is binomial
STEP 2: Create the probability distribution
|X |P(X) |
|0 | |
|1 | |
|2 | |
|3 | |
|4 | |
|5 | |
STEP 3: answer questions
P(X=2) = P(X ................
................
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