How many probability

What is the probability that there is at least one shared birthday among these 30 people? If you like to bet, and if you can convince 30 people to reveal their birthdays, you might be able to win some money by betting a friend that there will be at least two people with the same birthday in the room anytime you are in a room of 30 or more people.

This is one of many results in probability theory that is counterintuitive; that is, it goes against our gut instincts. If you keep track of the number of times that there is a repeated birthday, you should get a repeated birthday about 7 out of every 10 times you run the simulation. Suppose 10 people are in a room. What is the probability that there is at least one shared birthday among these 10 people?

Skip to main content. Module 8: Probability Theory. Search for:. Examples: Probability using Permutations and Combinations We can use permutations and combinations to help us answer more complex probability questions Example 1 A 4 digit PIN is selected. What is the probability that there are no repeated digits? Example 4 Compute the probability of randomly drawing five cards from a deck and getting exactly one Ace.

The solution is similar to the previous example, except now we are choosing 2 Aces out of 4 and 3 non-Aces out of 48; the denominator remains the same: It is useful to note that these card problems are remarkably similar to the lottery problems discussed earlier. Try it Now 2 Compute the probability of randomly drawing five cards from a deck of cards and getting three Aces and two Kings.

Example 6 Suppose three people are in a room. Example 7 Suppose five people are in a room. Example 8 Suppose 30 people are in a room. Question: I am playing a game with 5 possible outcomes.

It is assumed that the outcomes are random. For sake of his argument let us call the outcomes 1, 2, 3, 4 and 5. I have played the game 67 times. My outcomes have been: 1 18 times, 2 9 times, 3 zero times, 4 12 times and 5 28 times. I am very frustrated in not getting a 3. What are the odds of not getting a 3 in 67 tries? In a greater number of trials there may be an outcome of a 3 so the odds of not getting a 3 would be less than 1.

Question: What if someone challenged you to never roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of never getting a three? Question: I have a 12 digit keysafe and would like to know what is the best length to set to open 4,5,6 or 7?

Answer: If you mean setting 4,5,6 or 7 digits for the code, 7 digits would of course have the greatest number of permutations. Question: If you have nine outcomes and you need three specific numbers to win without repeating a number how many combinations would there be?

In general, if you have n objects in a set and make selections r at a time, the total possible number of combinations or selections is:. Not offhand. However I did a quick Google search for "games of chance probability books" and several were listed.

Maybe you could check them out on Amazon and there might be customer reviews. Thank you Eugene for this tutorial. Very Interesting!

Do you recommend any book which goes into more detail, ideally exploring games of chance, sports books etc? It's an "or" situation, so it's the probability of that event occurring in trial 1 or trial 2 or trial 3 etc up to trial If for instance you throw a dice and the event is getting a 6.

Then if the question was "what is the expectation of getting a 6 in each trial", then you would multiply the probabilities because it's an "and" situation. Thank you so much for this article. It was most helpful. It answered questions that bothered me since the days in college! Thanks LM, I learned this stuff in school over 30 years ago, but it was refreshing to revisit it! Thanks for sharing and reiterating the basic mathematics we learn in our early years of schooling!

Actually, this topic is very useful in real life even if you engange in a field which does not deal much on numbers such as mine. I agree with Jodah, well-researched hub! It's nice to know these equations and the odds of throwing certain numbers of dice, drawing a certain card etc. Very well researched hub , Eugene.

However under the heading "Probability of an Event" it says; "There are two types of probability, empirical and empirical.

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Online Learning. Social Sciences. Legal Studies. Political Science. Welcome to Owlcation. What Is Probability Theory? What's covered in this guide: Equations for working out permutations and combinations Expectation of an event Addition and multiplication laws of probability General binomial distribution Working out the probability of winning a lottery Definitions Before we get started let's review a few key terms. Probability is a measure of the likelihood of an event occurring.

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.

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See Subscription Options. Discover World-Changing Science. 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. You could also express the same results looking at heads landings for the same 10 tosses. Do your results match your expectations? Do another 10 coin tosses. Do you expect the same results? Why or why not? Compare your results from the second round with the ones from the first round.

Are they the same? Continue tossing the coin.