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Say you flipped the coin 10 times and came up with 3 heads. So, is the coin fair? How often can you expect to get heads if you flip a fair coin 10 times? You expect to get 0 heads about 0. It shows that when you flip a fair coin 10 times, you can pretty much get any outcome with reasonable probability. What if the same experiment is done by flipping the coin times? If a coin is flipped 10 times, the outcome can be anything from 0 to 10 heads. This is a transcript from the video series Understanding the Misconceptions of Science.
Watch it now, on The Great Courses Plus. The bottom line is that if you want to determine a probability, you need to gather a lot of statistics. One place where statistics is used a lot is in elections. On the other hand, there are hundreds of millions of possible voters.
However, the process is much trickier. Suppose, like is often in the case of US presidential election, the actual vote will be very close—very nearly Now, that might sound impossible, but suppose that the people that were asked were attending a National Rifle Association convention. You can never be sure, but it seems reasonable that NRA members might preferentially vote Republican. If you did the same exercise at a Greenpeace convention, you might find the opposite, with a majority of people being polled voting Democratic.
The point here is that it is extremely important when you do a statistical survey to pick an unbiased sample. In the case of polling for elections, you must select a small group of people who are similar, on average, to the typical voters. Historically, older, white, rural voters are more likely to go to the polls than younger, urban, ethnically diverse voters.
And pollsters have to take all of that into account in order to get an accurate prediction. The thing to keep in mind is that when you read a poll, try to find out if there are problems with how the poll was conducted.
If the number of people asked was pretty small, you have reasons to be suspicious of the conclusion. Similarly, if the poll was conducted by an organization that might select a group of people who differ from the likely voters, suspicions must arise there, too.
Thus, probabilities and polling results are things that are statistically complex and require a lot of analysis and a lot of data to be right. If you flip a fair coin twice, the possible outcomes are heads-heads, heads-tails, tails- heads, and tails-tails.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Flip a fair coin twice: eg. Here they are:. Then you can count for yourself how many subsets there are in the list that have zero elements, how many have exactly one element, how many have exactly two elements, and so forth.
When outcomes are assigned probabilities and are elements of a set, then any subset of the set is also called an event. The whole set itself is called the sample space. In general, if you want to break a set down into all of its subsets, you can use Pascal's Triangle or binomial coefficients to count them. Sign up to join this community.
The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Flip a fair coin twice Ask Question. Asked 3 years, 5 months ago. Active 3 years, 5 months ago. Viewed 2k times. I am confused of how the rest came to be. I was wondering if someone could please explain to me. Hidaw Hidaw 9 9 silver badges 30 30 bronze badges. That is, the event is a is a head resp. Active Oldest Votes.The outcomes from flipping a coin twice are the same as flipping two coins together.
So there are four possible outcomes. However, if you ask the question, "What is the chance of throwing a H with a T the probability is 2 out of 4 because there are two ways of doing that. Two possible outcomes for each flip. If you had n people, there would be 2n outcomes. The sample space consists of all the possible outcomes. A flip of a coin has 2 outcomes, H,T.
The total number of outcomes for 6 flips are 26 or Two mutually exclusive outcomes. You flip a coin, and only heads and tails are possible.
Otherwise, 4. If not, there are 5 outcomes 0 heads, 1 head, 2 heads, 3 heads and 4 heads. The odds of corerectly predicting 1 number on a dice with 1 throw is 1 in 6. Note: In flipping a coin, there are two possible outcomes at each flipping event.
The number of possible outcomes expands as a function of the number of times the coin is flipped. One flip, two possible outcomes. Two flips, four possible outcomes. Three flips, eight possible outcomes. Four flips, sixteen possible outcomes. It appears that the number of possible outcomes is a power of the number of possible outcomes, which is two. Looks like a pattern developing there.
Welcome to this variant of permutations. If each coin is a different color, then there are 32 possible outcomes. If you can't tell the difference between the coins, and you're just counting the number of heads and tails, then there are 6 possible outcomes: 5 heads 4 heads 3 heads 2 heads 1 heads all tails.
There are 2 possibilities for each toss. The result you're interested in is one of the four possibilities. Ok, sounds like a trick question. Obviously, there can be only one result, either heads or tails. Generally, when we consider the set of possible outcomes, we would say a coin flip has 2: a head and a tail. If I really want to complicate the matter, I could include that the coin might land on an edge. Don't think its realistic to include landing on an edge as an outcome.
If you roll a standard die and flip a penny at the same time, there are 12 possible outcomes. You can find this out quickly by multiplying the number of outcomes of the coin 2 by the number of outcomes of the die 6.It does matter, however, if you dictate that the first one must be head and the second one must be tail, or the first one must be tail and the second one must be head.
Then the probability becomes 0. Trending News. Lucille Ball's great-granddaughter dies at A warning sign for Trump at The Villages in Florida. Virginia health officials warn of venomous caterpillars. NBA star Kevin Love's honest talk about mental health.
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if you flip a coin twice what are you chances to get one heads and one tails?
Small town in Texas unites for justice for Jonathan Price. Corey E. What is the set of possible outcomes for this? Suppose you are going to flip a coin twice. Answer Save. Favorite Answer. For the first coin, it could be either head or tail. So the probability is 1. For the second coin, it has to be the opposite of the first. So the probability is 0. It doesn't matter if you use one coin and flip it twice or two coins and flip each on once. Rapidfire Lv 7. The chance of getting one head and one tail is one half.
If you flip a coin once the possible outcomes are heads or tails. If you flip a coin twice the possible outcomes both heads, both tails, or one head and one tail. How do you think about the answers? You can sign in to vote the answer.
Don't flip a coin twice. It's confusing.
Use this app instead. Still have questions?
It only takes a minute to sign up. This question has been asked and answered before here. However, my solution does not match the answer, and I want to know how my logic is wrong. I flip a fair coin 5 times in a row. What is the probability that heads never occurs twice in a row?
My approach: No two heads in a row means we also cannot have three heads in a row or four or five. Notice that these two events are equivalent:. The probability for heads occurring twice in the row equals the probability for tails occurring twice in a row. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.
Flip a fair coin 5 times. Ask Question. Asked 2 days ago. Active 2 days ago. Viewed 34 times. That is only true for independent events. I count five ways, not three. As pointed out by redroid, you would also have to worry about double counting if you proceeded in this way. Active Oldest Votes. Graham Kemp Graham Kemp k 6 6 gold badges 42 42 silver badges 98 98 bronze badges. Sign up or log in Sign up using Google.
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Email Required, but never shown. Featured on Meta. Responding to the Lavender Letter and commitments moving forward. Linked 5. Related 3. Hot Network Questions.An award-winning researcher, he as published in the leading refereed academic journals in Business and Economics and Theoretical and Applied Statistics. It relies on capturing relationships between explanatory variables and the predicted variables from past occurrences and exploiting this to predict future outcomes. Forecasting future financial events is a core actuarial skill.
Forecasting future financial events is a core actuarial skill - actuaries routinely apply predictive-modeling techniques in insurance and other risk-management applications.
This book is for actuaries and other financial analysts who are developing their expertise in statistics and wish to become familiar with concrete examples of predictive modeling. The book also addresses the needs of more seasoned practicing analysts who would like an overview of advanced statistical topics that are particularly relevant in actuarial practice. Predictive Modeling Applications in Actuarial Science emphasizes life-long learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used by analysts to gain a competitive advantage in situations with complex data.
It relies on capturing relationships between explanatory variables and the predicted variables from past.
The forecasting power of the global factor is above and beyond the predictive power contained in country-specific factors. As predicted by economic theories, bond return forecasts appear countercyclical. We also find that the global factor is related to international economic activity. Financial support from the Natural Science Foundation of China (Grant No. AbstractThis paper investigates the out-of-sample predictability of international bond risk premia.
We obtain predictive densities from a stae-of-the-art stochastic volatility (SV) model, which we then tilt towards the second moment of the risk-neutral distribution implied by options prices, while imposing a non-negativity constraint on the equity premium. By combining the backward-looking information contained in the SV model with the forward-looking information from options prices, our procedure delivers sharper predictive densities. Using density forecasts of the U. Series data maintained by Leslie Yancich (Obfuscate( 'brandeis.
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