Probability

REVISION Homework 2

CLASSICAL PROBABILITY number of favorable outcomes number of possible outcomes

Two Hypothesis : Equally likely outcomes and Finished outcomes

Property

P(Event) =

Probability is the measure of the likelihood that an event will occur

COMPLEMENTARY EVENTS

ADDITION RULE FOR DISJOINT EVENTS NOT DISJOINT EVENTS P(A or B) = P(A) + P(B) − P(A and B)

P(A or B) = P(A) + P(B)

P ( AT LAEAST ONCE E ) = 1 – P ( NEVER E)

Simple experiment

tree diagram : toss a coin

TREE DIAGRAM ROLL A DIE

Notes: the SUM of the probabilities of the individual events is 1 ( Total Probability)

on the branches you must write the probability

Deck of 52 Cards SUITS: hearts (♥) , diamonds (♦) spades (♠) and clubs (♣)

Each suit has 10 numbered cards and 3 figures : jack, queen and king.

Choose at random a ball from a bag

notes: the SUM of the probabilities of the individual events is ONE (Total Probability)

Green Red Yellow

5 RED, 3 GREEN, 2 YELLOWS BALLS

Experiments with

repeated trials

the sample space is given by S = { HH, HT, TH, TT}

TOSS TWO COINS

TOSS THREE COINS

ROLL TWO DICE AND ADD THE SCORES : TABULAR FORM

Rolling a Die and tossing a Coin If you roll a die and toss a coin: a) which is the number of the possible outcomes? b) represent the situation with the tree diagram and then with the tabular form What is the probability of obtaining:

c) five and a Head d) five or Head e) an even number and Tail

TRY IT YOURSELF

TREE DIAGRAMM : COIN -DIE

TREE DIAGRAMM : COIN -DIE