What is the difference between how many and probability

It was in the seventeenth century that gamblers asked famous mathematician Blaise Pascal and Pierre de Fermat to help them in knowing their chances of winning in these games. Today help of probability is being taken in many fields such as finance, medicine, genetics, marketing, sociological surveys and even science to predict the outcome of an event.

Exit polls in elections are the result of probability. Your email address will not be published. Leave a Reply Cancel reply Your email address will not be published. The same holds true for 2, and for 3, and for 5, and for 6. The single-event probability that a roll of the die will result in any one face you select is 1 in 6.

Cumulative probability measures the odds of two, three, or more events happening. There's just one catch involved: each event needs to be independent of the others—you can't have two events that occur at the same time, or have the outcome of a first event influence the probability of the next which would be conditional probability. An easy way to get the concept of independence is to think about tossing a coin: for any one toss, it cannot land on both heads and tails, right?

Moreover, getting a head or a tail on your first toss has no effect on whether you get a head or tail on your second toss. So tossing a coin is an independent event. The events in cumulative probability may be sequential, like coin tosses in a row, or they may be in a range. For example, if you're observing a response with three categories, the cumulative probability for an observation with response 2 would be the probability that the predicted response is 1 OR 2. So to find the odds of ONE of these two events occurring, we add—or accumulate —the chances of either one occurring.

If all this sounds a little confusing, that's okay. We can very easily illustrate the difference between cumulative and single-event probability by putting the data for rolling a die into a table.

The table below shows the probability of getting a selected face value 1 through 6 when you throw a single die; the cumulative probability of getting a selected face value or less when you throw a single die; and finally the cumulative probability of getting a selected face value when you throw 1 to 6 separate dice or 1 die up to six times.

Cumulative Probability of rolling face value or less on a single die odds of 1, 2, or more events. That's a single-event probability.

But if we roll the die and want to know the probability that we will roll a 1 or a 2, that's cumulative probability, because it is the accumulated value of the odds of one OR the other happening. What if we throw the die multiple times? You will find out by tossing a coin and rolling a die in this activity. Observations and Results Calculating the probabilities for tossing a coin is fairly straightforward.

A coin toss has only two possible outcomes: heads or tails. Both outcomes are equally likely. This means that the theoretical probability to get either heads or tails is 0.

The probabilities of all possible outcomes should add up to 1 or percent , which it does. When you tossed the coin 10 times, however, you most likely did not get five heads and five tails. In reality, your results might have been 4 heads and 6 tails or another nonand-5 result.

These numbers would be your experimental probabilities. In this example, they are 4 out of 10 0. When you repeated the 10 coin tosses, you probably ended up with a different result in the second round.

The same was probably true for the 30 coin tosses. Even when you added up all 50 coin tosses, you most likely did not end up in a perfectly even probability for heads and tails.

You likely observed a similar phenomenon when rolling the dice. Instead of rolling each number 17 percent out of your total rolls, you might have rolled them more or less often. If you continued tossing the coin or rolling the dice, you probably have observed that the more trials coin tosses or dice rolls you did, the closer the experimental probability was to the theoretical probability.

Overall these results mean that even if you know the theoretical probabilities for each possible outcome, you can never know what the actual experimental probabilities will be if there is more than one outcome for an event.

This activity brought to you in partnership with Science Buddies. Already a subscriber? Sign in. Thanks for reading Scientific American. Create your free account or Sign in to continue. See Subscription Options. Go Paperless with Digital. Materials Coin Six-sided die Paper Pen or pencil Preparation Prepare a tally sheet to count how many times the coin has landed on heads or tails.

Prepare a second tally sheet to count how often you have rolled each number with the die. Procedure Calculate the theoretical probability for a coin to land on heads or tails, respectively.

Write the probabilities in fraction form. What is the theoretical probability for each side? Now get ready to toss your coin. Out of the 10 tosses, how often do you expect to get heads or tails? Toss the coin 10 times. After each toss, record if you got heads or tails in your tally sheet.

Count how often you got heads and how often you got tails. Write your results in fraction form. The denominator will always be the number of times you toss the coin, and the numerator will be the outcome you are measuring, such as the number of times the coin lands on tails.