Is it possible to have probability greater than 1

We also know the first card was an ace, therefore:. As an example, consider the experiment of rolling a die and flipping a coin. To say that two events are independent means that the occurrence of one does not affect the probability of the other. In probability theory, to say that two events are independent means that the occurrence of one does not affect the probability that the other will occur.

The concept of independence extends to dealing with collections of more than two events. To show that two events are independent, you must show only one of the conditions listed above. If any one of these conditions is true, then all of them are true. Translating the symbols into words, the first two mathematical statements listed above say that the probability for the event with the condition is the same as the probability for the event without the condition. For independent events, the condition does not change the probability for the event.

As an example, imagine you select two cards consecutively from a complete deck of playing cards. The two selections are not independent. The result of the first selection changes the remaining deck and affects the probabilities for the second selection.

Because the deck of cards is complete for both selections, the first selection does not affect the probability of the second selection. When selecting cards with replacement, the selections are independent. Independent Events: Selecting two cards from a deck by first selecting one, then replacing it in the deck before selecting a second is an example of independent events. Consider a fair die role, which provides another example of independent events.

If a person roles two die, the outcome of the first roll does not change the probability for the outcome of the second roll. Two friends are playing billiards, and decide to flip a coin to determine who will play first during each round. For the first two rounds, the coin lands on heads. They decide to play a third round, and flip the coin again.

What is the probability that the coin will land on heads again? First, note that each coin flip is an independent event. The side that a coin lands on does not depend on what occurred previously. Also recall that the following statement holds true for any two independent events A and B:. The experimental probability is the ratio of the number of outcomes in which an event occurs to the total number of trials in an experiment. The experimental or empirical probability pertains to data taken from a number of trials.

It is a probability calculated from experience, not from theory. Experimental probability contrasts theoretical probability, which is what we would expect to happen. We know that this is unlikely to happen in practice.

If we conduct a greater number of trials, it often happens that the experimental probability becomes closer to the theoretical probability. Similarly an 'impossible' event can never occur, such as the chance of pulling a black ball from a bag of green balls. It simply cannot happen. In decimal notation, this is a probability of 0. The terms 'likely' and 'unlikely' mean a probability of greater than and less than 0. We can show this information on a probability diagram:.

In the example in the previous section, we talked about the probability of rolling a number less than 9 and decided it was certain. Active Oldest Votes. Bram28 Bram28 Then What formula should I use to calculate probability of getting at least one tail from my original question?

Show 3 more comments. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Asked 11 years ago. Active 4 months ago. Viewed k times. Improve this question. Wikipedia should correct that entry. The CDF is a lot more intuitive to use in many cases. Add a comment. Active Oldest Votes.

Improve this answer. Extending this, if one doesn't want to assume normality but instead one has empirical data from which density can be estimated, e. It's unclear how a kde could be construed similarly, but I'm no expert in this area.

Your question is interesting enough that you might consider posting it separately. What If you had picked a differential of 1 instead? Sorry for my confusion here. Can you explain? Show 7 more comments. See What is a probability distribution : continuous probability functions are defined for an infinite number of points over a continuous interval, the probability at a single point is always zero.

Tristan Tristan 1, 10 10 silver badges 12 12 bronze badges. It would be better for them just to omit the first sentence in the quotation. If the probably was "always zero" then, by definition , no such result would be possible. Mark L.