Math and Arithmetic

Statistics

Probability

Top Answer

Anyone can flip a coin four times so I say 100 percent probability. On the other maybe you should ask the odds of the results from four flips.

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0Experimental probability is calculated by taking the data produced from a performed experiment and calculating probability from that data. An example would be flipping a coin. The theoretical probability of landing on heads is 50%, .5 or 1/2, as is the theoretical probability of landing on tails. If during an experiment, however, a coin is flipped 100 times and lands on heads 60 times and tails 40 times, the experimental probability for this experiment for landing on heads is 60%, .6 or 6/10. The experimental probability of landing on tails would be 40%, .4, or 6/10.

The difference between experimental probability and theoretical probability is that experimental probability is the probability determined in practice. Theoretical probability is the probability that should happen. For example, the theoretical probability of getting any single number on a number cube is one sixth. But maybe you roll it twice and get a four both times. That would be an example of experimental probability.

The theoretical probability of rolling a 5 on a standard six sided die is one in six. It does not matter how many times you roll it, however, if you roll it 300 times, the theoretical probability is that you would roll a 5 fifty times.

50/50 50/50? This is equal to 1 which would imply the probability of flipping a head is certain. Obviously not correct as the probability of flipping a head in a fair dice is 1/2 or 0.5

Take for example, flipping a coin. Theoretically, if I flip it, there is a 50% chance that I flip a head and a a 50% chance that I flip a tail. That would lead us to believe that out of 100 flips, there should theoretically be 50 heads and 50 tails. But if you actually try this out, this may not be the case. What you actually get, say 46 heads and 54 tails, is the experimental probability. Thus, experimental probability differs from theoretical probability by the actual results. Where theoretical probability cannot change, experimental probability can.

Theoretical probability = 0.5 Experimental probability = 20% more = 0.6 In 50 tosses, that would imply 30 heads.

If you roll a die 100 times, you would expect to get a 1 about 17 times, because the probability of getting a 1 is 1 in 6, or 0.1667. However, that is theoretical probability; experimental probability - the actual results of doing this 100 times - might not be 17, but if you did this a large number of times, the experimental results would indeed begin to approach the theoretical results.

The empirical probability can only be determined by carrying out the experiment a very large number of times. Otherwise it would be the theoretical probability.

1/2 if the quarter is 'fair'.

There are five letters, and two of them are s's. The theoretical probability of choosing an s would be 2 out of 5.2/5 or 40%

It is neither. If you repeated sets of 8 tosses and compared the number of times you got 6 heads as opposed to other outcomes, it would comprise proper experimental probability.

These would be independent events; therefore, we can multiply the probabilities of each of the two events. Probability of flipping a head: 1/2 Probability of rolling an odd number with a single die: 1/6 Required probability : 1/2 x 1/6 = 1/12

None, since that would imply that in 18 cases the coin did not show heads or tails!

You take the probability of each event and multiply them. In the case of the given example, your odds or flipping a head and rolling a 5 would be 1/2 * 1/6, which equals 1/12.

In experimental probability the probabilities of the outcomes are calculated as the proportion of "successful" outcomes in repeated trials. In theoretical probability these are calculated on the basis of laws of science being applied to a model of the experiment. For example, to find the probability of rolling a six on a standard die, you could roll the die many times (N) and count the number times that it comes up 6 (n). The experimental probability is n/N. The theoretical approach would be to work from the principle that each outcome was equally likely - since it is a fair die - and since the total probability must be 1, the probability of any one face must be 1/6. The second method will only work if there is a good mathematical model.

Complementary events are events that are the complete opposite. The compliment of event A is everything that is not event A. For example, the complementary event of flipping heads on a coin would be flipping tails. The complementary event of rolling a 1 or a 2 on a six-sided die would be rolling a 3, 4, 5, or 6. (The probability of A compliment is equal to 1 minus the probability of A.)

When you know for sure that the data you are trying to describe has a well-known theoretical probability distribution. For example, you 'know' from past experience that the heights of a certain age group in a school is normally distributed.

In order to answer this question it is important, first, to be certain that the theoretical probability (not probality!) can be calculated. For example, there is a probability that the first car that I see being driven on the next day [tomorrow] is black but I challenge anyone to calculate the theoretical probability. No one, not even I, know when I will wake up tomorrow (assuming that I live to wake up), when I draw my curtains and when look into the street. The number of black cars and non-black cars in my locality can be found, but it could be a car from somewhere else which just happens to drive past at the critical moment.Assuming there was a theoretical probability, the experimental probability would be better than would be obtained from 999 trials and not as good as 1001 trials. Any other statements would depend on the distribution of the variable being observed.

The term "theoretical probability" is used in contrast to the term "experimental probability" to describe what the result of some trial or event should be based on math, versus what it actually is, based on running a simulation or actually performing the task. For example, the theoretical probability that a single standard coin flip results in heads is 1/2. The experimental probability in a single flip would be 1 if it returned heads, or 0 if it returned tails, since the experimental probability only counts what actually happened.

Multiply together the probability that each event would have of occurring by itself. For example, the probability of rolling a "3" on a single die is 1/6 ,because there are 6 different possibilities. And the probability of flipping a "heads" on a coin is 1/2 , because there are two possibilities. Then the probability of rolling a "3" AND flipping a "heads" is ; 1/6 x 1/2 = 1/12 .

The theoretical probability that a tribute from 1,2,4 will win the Hunger Games is 25% chance. To find the experimental probability you would have to know which tributes won in the last 75 hunger games to know there chance of winning in the future.

First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.Or, of course, it could be a mixture of both.First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.Or, of course, it could be a mixture of both.First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.Or, of course, it could be a mixture of both.First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.Or, of course, it could be a mixture of both.

Since there are 6 numbers on a die (1-6), then the probability of rolling a 5 would be 1 out of 6.

The probability of flipping a coin 24 times and getting all heads is less than 1 in 16 million. (.524) It would seem that no one has ever done that.

The probability of drawing the Ace of Spades from a standard deck of 52 cards is 1 in 52, or about 0.01923. However, the number of times you can expect to draw it depends on random statistics. If you tested this a large number of times, shuffling the deck each time, you would expect about 1 out of every 52 trials to be the Ace of Spades, but that would only be in the long run, say for thousands and thousands of trials, and even then, it would not be exact. This is the difference between theoretical probability and experimental probability. Theoretical probability is based on pure statistics and the arrangement of the test. All you can say is that, for an infinite number of trials, you would expect 1 out of 52. In the case of experimental probability, you are limited by the number of trials that you can perform. Lets say you ran 10,000 trials. Theoretically, you would expect to draw the Ace of Spades about 192 times. In practice, you would have a range of results.

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