Risk is when an outcome’s probability is known. Uncertainty is when an outcome’s probability is unknown.

Phone NumbersA computer is used to generate random telephone numbers. Of the numbers generated and in service, 56 are unlisted and 144 are listed in the telephone directory. If one of these telephone numbers is randomly selected, what is the probability that it is unlisted?

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The probability that Gallant Fox will win the first race is 2/5 and that Nashau will win the second race is 1/3.

3. What is the probability that at least one horse will win a race?

2. What is the probability that both horses will lose their respective races?

1. What is the probability that both horses will win their respective races?

Chad has arranged to meet his girlfriend, Stephanie, either in the library or in the student lounge. The probability that he meets her in the lounge is 1/3, and the probability that he meets her in the library is 2/9.

a. What is the probability that he meets her in the library or lounge?

b. What is the probability that he does not meet her at all?

Mutually Exclusive Events ...Two events are mutually exclusive (or disjoint) if it is impossible for them to occur together.

Examples:1. Experiment: Rolling a die once Sample space S = {1,2,3,4,5,6} Events A = 'observe an odd number' = {1,3,5} B = 'observe an even number' = {2,4,6} A ∩ B = ∅ (the empty set), so A and B are mutually exclusive.

Mutually Exclusive Not Mutually Exclusive

Formally, two events A and B are mutually exclusive if and only if

Mutually Exclusive Events ...Two events are mutually exclusive (or disjoint) if it is impossible for them to occur together.

Examples:1. Experiment: Rolling a die once Sample space S = {1,2,3,4,5,6} Events A = 'observe an odd number' = {1,3,5} B = 'observe an even number' = {2,4,6} A ∩ B = ∅ (the empty set), so A and B are mutually exclusive. 2. A subject in a study cannot be both male and female, nor can they be aged 20 and 30. A subject could however be both male and 20, or both female and 30.

Mutually Exclusive Not Mutually Exclusive

Formally, two events A and B are mutually exclusive if and only if

ExampleSuppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards.

We define the events A = 'draw a king' and B = 'draw a spade'Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have:

P(A U B) = P(A) + P(B) - P(A ∩ B) = 4/52 + 13/52 - 1/52 = 16/52

So, the probability of drawing either a king or a spade is 16/52 = 4/13.

Identify the events as:

a. A bag contains four red and seven black marbles. The event is randomly selecting a red marble from the bag, returning it to the bag, and then randomly selecting another red marble from the bag.

b. One card - a red card or a king - is randomly drawn from a deck of cards.

c. A class president and a class treasurer are randomly selected from a group of 16 students.

d. One card - a red king or a black queen - is randomly drawn from a deck of cards.

e. Rolling two dice and getting an even sum or a double.

independent

dependent mutually exclusive

not mutually exclusiveDrag'n Drop

Baby!

independent mutually exclusive

not mutually exclusiveindependent

dependent mutually exclusive

independentmutually exclusive