12.1/12.2 probability quick vocab: random experiment: “random” act, no way of knowing ahead of...
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12.1/12.2 Probability
Quick Vocab:
Random experiment: “random” act, no way of knowing ahead of time
Outcome: results of a random experiment Event: a set of outcomes Sample space: the set ALL possible
outcomes
Probability
P(Event) = P(E)
Toss of coin:
Probability of landing on heads:
P(H) =
# of outcomes in the event
# of total outcomes in the sample space
1
2
“Probability of an event”
Probability
P(will definitely occur) = 1ex: Have 1 die
P(never occur) = 0ex: Have 1 die
= 1P(roll a #)
P(roll a letter) = 0
Probability
Two dice are rolled and the numbers are noted. Find the probability of each event.
a) The sum of the numbers is less than 5
Possibilities when 2 dice are rolled(Pg. 632 in book)
Sum < 5 ?
TOTAL = 36
Probability
Two dice are rolled and the numbers are noted. Find the probability of each event.
a) The sum of the numbers is less than 5
b) The sum of the numbers is 4 or 5.
6
361
6
Possibilities when 2 dice are rolledSum = 4 or 5 ?
Probability
Two dice are rolled and the numbers are noted. Find the probability of each event.
a) The sum of the numbers is less than 5
b) The sum of the numbers is 4 or 5.
6
361
6
7
36P(4 or 5) =
Standard Deck of Cards
52 cards in the deck26 black, 26 red4 suits: hearts, diamonds, clubs, spades
13 of each suitFace cards: Have a FACE!! (not Ace)
Clubs(Black)
Hearts(Red)
Diamonds(Red)
Spades(Black)
A card is drawn from a standard deck of 52 cards.
What is the probability that the following occurs?
P( a red card)
# of red cards in deck?
P(a spade)
# of s in deck?
26 26
52
13
5213
1
2
1
4
A card is drawn from a standard deck of 52 cards.
What is the probability that the following occurs?
TOO: P(the card is a heart)
# of s in deck?
P(the card is a 3 or 4)
# of 3s? # of 4s?
13
13
521
4
4 4
8
522
13
A card is drawn from a standard deck of 52 cards.
What is the probability that the following occurs?
TOO: P(between a 2 and 5, inclusive)
# of each ? 416 4
52 13
2, 3, 4, and 5: 4 x 4=16
A nickel, dime and quarter are flipped. H=heads, T=tails
How many elements are in the sample space?
Find P(exactly 2 tails)
P(nickel or dime are heads)
8HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
3
8
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT6 3
8 4
A nickel, dime and quarter are flipped. H=heads, T=tails
TOO: Find P(at least 2 tails)
P(4 heads)
4 1
8 2
HHH, HHT, HTH, THH, TTH, THT, HTT, TTT
00
8
Homework
Pg. 633 #1-13, Pg. 635-636 Q1-10, 1 & 2