Suppose that RHS is 58% male. What is the probability that the first girl to walk through the front doors is the 6th person? (assume independence)

Transcription

1 Problem of the Day Suppose that RHS is 58% male. What is the probability that the first girl to walk through the front doors is the 6th person? (assume independence)

2 Problem of the Day Suppose that RHS is 58% male. (assume independence) What is the probability that 4 of the first 10 people to walk through the door are girls? What is the probability that at least 4 of the first 10 people to walk through the door are girls?

3 Problem of the Day Suppose that RHS is 58% male. What is the probability that at least 4 of the first 10 people to walk through the door are girls? (assume independence)

4 Problem of the Day A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves 6 times, what s the probability she gets a) all 6 serves in? b) exactly 4 serves in? c) at least 4 serves in? d) no more than 4 serves in?

5 Problem of the Day American Airlines believes that only 5% of passengers fail to show up for flights. For this reason they overbook flights. They will sell 275 tickets for a plane with 265 seats. What is the expected number of passengers who will show up? Find the standard deviation. What is the probability that only 266 people show up? What is the probability that more than 265 show up?

6 Problem of the Day Do these situations involve Bernoulli trials? When Joe plays basketball, the probability that he makes any given free throw is 2/3. You go into business selling bagels, but your oven is unreliable and burns every 8th bagel on average. Moreover, your little brother (whom you have hired to do the baking and packaging) puts burned and unburned bagels alike into the bags of bagels you sell. Green eye color is present in about 2% of the population. Blue eye color is present in about 30% of the population. Record the eye colors of students who enter RHS.

7 Chapter 17 Probability Models Bernoulli Trials you know the probability of success(and failure) same on every trial(like with replacement) trials are independent The probability of a Honda Civic electrical malfunction is 1.7%. What is the probabilility you get 19 working Civics before a defective one?

8 10% condition If Bernoulli trials are not independent, it is still ok to proceed if the sample is smaller than 10% of the population

9 The probability of getting an F on Mr. Stalter's quizzes is.10. How many quizzes would it take to "guarantee" an F?

10 Geometric Probability Model models the calculations used in Bernoulli trials p = X = σ

11 The vast majority of is considered "spam" , over 91% of it actually. Without spam filters we would be drowning in spam. What is the probability that the 5th is the first "real" ? If you did not have a spam filter, how many s would you expect to open before getting a "real" ? What is the standard deviation of the number of s before a "real" ?

12 O negative blood appears in about 6% of the population. What is the probability that the 10th person is the first with O negative blood? At the JROTC blood drive, how many people do you expect to give blood before you find someone with O negative blood?

13 The vast majority of is considered "spam" , over 91% of it actually. Without spam filters we would be drowning in spam. What about the probability that 3 out of 10 s are "real" s?

14 Combinations: order doesn't matter!!!!!!!!! finding the number of ways an event can happen we will say k successes in n trials nc k ncr(n,r) Number of different committees of 3 that Ms. Reed can make from 6 council members Number of ways I can be tardy to 2 of my 7 classes Number of ways that I can get 4 Aces in a 5 card poker hand

15 Student council consists of 3 boys and 3 girls. Find the probability that Ms. Reed forms a 3 person committee with 2 boys. I am tardy 15% of the time. Find the probability that I am tardy to 4 of my 7 classes. Find the probability of getting 4 Aces in a poker hand.

16 Practice Problems Your new restaurant specializes in Vegetarian cuisine. If 1.3% of the population considers themselves vegetarian, answer the following. Find the probability that 5 of the next 7 customers are actually vegetarians Would you be surprised if only 1 out of the next 10 people was a vegetarian? What is the probability that at least 2 of the next 5 people are vegetarians?

17 Practice Problems Your new restaurant specializes in Vegetarian cuisine. If 1.3% of the population considers themselves vegetarian, answer the following. How many customers do you expect before you find someone who is a vegetarian?

18 The vast majority of is considered "spam" , over 91% of it actually. Without spam filters we would be drowning in spam. How many spam s do you expect out of 10?

19 Binomial Probability n = p = X = P(X = k) = σ

20 WacArnolds is running a "Free Cheeseburger" promotion where 45% of large drinks come with a coupon for a free cheeseburger. If you buy 10 large drinks what is the probability that you get 5 free cheeseburgers?

21 Approximating Binomial Probabilities A binomial model is approximately normal if... WacArnolds is running a "Free Cheeseburger" promotion where 45% of large drinks come with a coupon for a free cheeseburger. If you buy 10 large drinks what is the probability that you get at least 5 free cheeseburgers?

22 Practice Problem About 2.1% of Richwoods students get referrals for something other than tardies. Suppose you ask 1000 students, what is the probability that more than 4 have a referral for something other than tardies?

23 Your annoying little brother is flipping a fair coin but claims that it is "Magic" such that heads is more likely. Out of 100 flips, what would it take to convince you that it is truly "Magic"???? Find the probability for your assertion and adjust it as necessary.

24 Readings and Examples pgs Homework: pgs 402 4:7,9,13,15,17,19,21,23,31,35,38

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26 Exit Slip WacArnolds is running a "Free Cheeseburger" promotion where 45% of large drinks come with a coupon for a free cheeseburger. Decide whether this is a geometric model or binomial model. Find the mean and standard deviation for the number of drinks you would expect to buy in order to get a free cheeseburger.

27 You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total for all the rolls. But... if you roll a 6, your score is 0 and your turn is over. What might be a good strategy for a game like this? a) On what roll would you expect to get a 6 for the first time? b) So, roll one time less than that. Assuming all those rolls were not 6 s, what s your expected score? c) What s the probability that you can roll that many times without getting a 6?

28 Suppose that 70% of the women who suspect they may be pregnant and purchase an in home pregnancy test are actually pregnant. Further suppose that the test is 98% accurate. What s the probability that a woman whose test indicates that she is pregnant actually is?