natalia sivackova introduction to probability. equally likely events coin toss example: probability...

NATALIA SIVACKOVA

Introduction to Probability

Equally Likely Events

Coin toss example:Probability of result is ½

Dice example:Probability of result is 1/6

For nth termProbability = 1/n

Not Equally Likely Events

Bag of marbles4 blue5 green6 red

Probability of picking blue?4/15

General Formula

The bag is Un(U) = 15

Blue marbles form a subset A UProbability of picking a member of A is P(A)

P(A) = n(A)/n(U)

Probability of a Complementary Event

Sock drawer contains 53 socks13 are single socks40 are in a pair

Probability of single sock: n(S)/n(U) = 13/53Probability of a sock from a pair: n(S’)/n(U) =

P(S) + P(S’) = 53/53 = 1

Generalized formula for all subsets: P(S’) = 1 – P(S)

S S’ = U

When an event is certain it has a probability of 1When an event is impossible it has a probability

(e.g. of an impossible event)S S’ =

(You cannot pick a sock that is both single and part of a pair)

Documents