How likely is it that…..?

The Law of Large Numbers says that the more times you repeat an experiment the closer the relative frequency of an event will come to the theoretical probability of the event. Let’s try an experiment: Flip a coin 20 times and record how many heads and how many tails….

Experiment 3: A single die is rolled S={1, 2, 3, 4, 5, 6}

Try it! There are 11 possible outcomes. Are they equally likely?

How likely is it that two of us have the same birthday?

How many people must be in the room before the probability that two have the same birthday is more than ½?

A little Vocabulary for some common sense ideas:

Two events are Mutually Exclusive if they cannot occur simultaneously. For example in the experiment where you roll a pair of dice, the event that you roll 12 and the event that you roll 2 are mutually exclusive. If events A and B are Mutually exclusive then the probability that A OR B occurs is P(A) + P(B). Of course the probability that A AND B occurs is 0!

Two events are Independent if knowing that one has occurred does not effect the probability that the other will occur. If I flip a penny and a nickel simultaneously the event that the penny comes up heads and the event that the nickel comes up heads are independent. We assumed that the sex of the children of our alumni friends were independent and that our birthdays were independent. If A and B are independent the probability that A AND B occur is P(A and B) = P(A)P(B) we used this in the birthday problem

A few sample problems from Ask Marylyn

Suppose 95% of a given population are not drug users and that a drug test has a 95% chance of returning the correct result. a) What is the probability an individual chosen at random from the given population will test positive for drugs? b) Given that an individual from this population has tested positive for drugs, what is the probability that the person uses drugs? c) What is the probability that a non- drug user will test positive?

Binomial Distributions A Probability Experiment