Chapter 17-1

Chapter 17-1 - Chapter 17 Probability Models 1 Bernoulli...

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Chapter 17 Probability Models 1. Bernoulli Trials (properties) Two possible outcomes (success and failure) The probability of success, denoted by p, is the same on every trial The trials are independent Example: Suppose 75% of all drivers wear their seatbelts. Find the probability that four drivers might be belted among five cars waiting traffic light?

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Chapter 17 Probability Models 2. The Geometric Model: How many trials are needed to observe the first success? Let p = probability of success, q = 1-p be probability of failure, X= be the number of trials until the first success occurs. Then P(X=x) q^{x-1}p Expected value E(X) = 1/p Std deviation of X = Sqrt(q/p^2)
Chapter 17 Probability Models Example: People with O-negative blood type are called universal donors. Only about 6% of people have O-negative blood. If donors line up at random for blood drive, a) how many do you expect to examine before you find someone who has O-negative blood? b) What’s the probability that the first O-negative donor found is one of the four people in line?

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Chapter 17 Probability Models a) E(X) = 1/0.06 = 16.6 On average a universal donor is found by examining 16.7 people. b) P(X <= 4) = P(X=1)+ P(X=2)+ P(X=3)+ P(X=4) 0.2193
Chapter 17 Probability Models 3. The Binomial Model: The binomial model is like a Bernoulli trial with a number of trials being n, n is a number greater than or equal to 2. We look for the number of k successes in n trial. Here k is less than or equal to n. Let X = number of successes in n trials.

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Chapter 17 Probability Models P(X=x) = C(n,x)*p^x*q^{n-x} Here p = probability of success, q = 1-p = probability of failure. E(X) = np Std dev of X = Sqrt{npq}
Chapter 17 Probability Models Example: Suppose 20 people come to the blood drive. What is the probability that there are 2 or 3 universal donors? Solution: P(X=2) = C(20,2)(.06)^{2}(.94)^{18}= 0.2246 P(X=3) = C(20,3)(.06)^{3}(.94)^{17}= 0.0860 Answer: 0.3106

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Chapter 17 Probability Models To compute the C(n,x) number from the TI-83 do the following 1. Type your number 2. Press MATH 3. Select Prob 4. Press nCr 5. Type your second number
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Chapter 17-1 - Chapter 17 Probability Models 1 Bernoulli...

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