Statistic: Chapter 17

A probability of any outcome of a random phenomenon is a number between:

0 and 1

From a computer simulation of rolling a six-sided die ten times, the following data were collected based on the number of spots showing: 5 5 1 3 2 1 5 6 5 1 This means the probability of rolling 4 is 1/_____ .

6 Not having seen a four on these 10 rolls does not mean it won't happen. The die is balanced so the probability is 1/6 which is approximately 0.17.

Which of the following statements is true? (Mark all that apply).

An outcome with a probability 1 happens on every repetition. An outcome with probaility one half, or 1 in 2, happens approximately half the time in a very long series of trials. An outcome with a probability 0 never occurs. As the probability of an outcome gets closer to one, an outcome is more likely to occur.

Which of the following correctly explains why the following statement is true or false: "The probability that a child delivered in a certain hospital is a girl is 0.50, so over the next 100 births, there will be equal numbers of boys and girls born at that hospital."

False. Probability addresses what will happen over a very long period of time, but 100 births is a short time frame. Probability addresses what will happen over a long period of time, not short time frames. 100 births is still a short time frame.

Which of the following is NOT an example of a personal probability?

If Terence tosses a fair six-sided die, the chance it will land on a five is around 17%. The number (1 in 6, or 17%) is based on long-term relative frequency, not opinion.

The mistake of believing that, in 6 spins of the roulette wheel, the sequence RBRBBR is more likely than RRRBBB (where R is red and B is black) is an example of the _____.

Myth of short run regularity Probability is random in the long run but not random in the short run. Thus, both sequences are equally likely in the short run.

The mistake of believing that, in 6 tosses of a fair coin, the sequence THTHHT is more likely than TTTHHH (where T is tail and H is head) is an example of the _____.

Myth of short run regularity Probability is random in the long run but not random in the short run. Thus, both sequences are equally likely in the short run.

Ryan is playing a game where he is trying to predict if a coin will be a heads or a tails. He flips a fair coin 5 times and gets heads all five times. On the next flip, he says that the coin HAS to land on tails because of all of the previous heads. What myth is Ryan falling victim to?

Myth of the law of averages He is mistakenly assuming that if one heads occurs several times, then it becomes increasingly more likely that the next one should be tails. This is the myth of the law of averages.

Sam is playing a game where he is trying to predict if a fair die will land on a certain number. He tosses a six-sided die 5 times and gets ones all five times. On the next toss, he says that the die HAS to land on anything but a one because of all of the previous ones. What myth is Sam falling victim to?

Myth of the law of averages He is mistakenly assuming that if one number occurs several times, then it becomes increasingly more likely that the next one should be different. This is the myth of the law of averages.

Frank was watching a professional football game on Sunday and noted that the final score was 10-17. This coincidently was the price of his lunch that day ($10.17). Believing that these two event occurring simultaneously is extremely rare is to fall victim to the _____.

Myth of the surprising coincidence There are many professional football games each Sunday during football season and 10-17 is a relatively common score. Also, having a lunch of $10.17 is not extremely uncommon. He has fallen prey to the myth of the surprising coincidence.

Which of the following is a correct interpretation the statement, "The probability that a child delivered in a certain hospital is a girl is 0.50"?

Over a long period time, there will be equal proportions of boys and girls born at that hospital. Probability addresses what will happen over a long period of time, not short time frames.

Susan always takes the bus when she goes downtown because she claims the chances of finding a parking spot are around 5%. Susan's belief is an example of a _____.

Personal probabilities This number is based on judgement, not long-term models.

Which of the following events would NOT be considered a random phenomenon?

The event that a person with vision impairment wears glasses. Glasses are designed to correct vision impairment, so wearing glasses when one has such an impairment is not random.

We can never observe a probability exactly.

True

Why do we worry about very unlikely threats such as tornadoes and terrorists more than we worry about heart attacks?

We feel safer when a risk seems under our control than when we cannot control it. It is hard to comprehend very small probabilities

The personal probability of an outcome is...

a number between 0 and 1 that expresses an individual's judgment of how likely the outcome is.

Personal probabilities have the great advantage that they are not __________ to repeatable settings.

limited

An outcome with a probability of .89 means that the outcome _____.

often occurs A probability of .89 means that the outcome occurs often but will not always occur.

Your friends follow the Chicago Cubs baseball team. Donna says that she feels the chance they will make the World Series this year is 25%. This is an example of personal _____.

probability The number is based on her beliefs, not a long series of repeated trials, so it is personal probability.

An event is _____ if individual outcomes are uncertain but happen in a predictable manner through time.

random Randomness means that we do not know what will happen on any one trial, but over the long run, a pattern of sorts emerges.

Chance behavior is ________ in the short run but has a ______ and _________ pattern in the long run.

unpredictable regular predictable

Personal probabilities are numbers between _____ and 1, inclusive.

zero Probability is the proportion of times the outcome would occur in a very long series of repetitions. It cannot be negative and is never bigger than 1.