Download 4.2 Notes - morgansmathmarvels

Notes 4.2
Probability
Rules
I.
“And” Compound Probabilities – the chance of two or
more events ___________________________.
A. If the events are independent (outcome of the first
event ________________ the outcome of the second event),
then
P(A and B) =
Ex. 1 A card is randomly drawn from a standard deck of 52
cards, then replaced. Then a second card is randomly
drawn. Find the probability of the following:
a) the first card is an eight and the second card is a
queen.
P(8, Q) =
b) both cards are hearts.
P(Heart, Heart) =
c) first card is black and the second card is not a face
card (jack, queen, or king).
P(Black, Not Face) =
Ex. 2 A bag contains 20 marbles: 8 red, 5 blue, 4 green, and
3 yellow. A marble is drawn at random, replace, then a
second marble is drawn. Find the probability of the
following:
a)
P(Red, Green) =
b)
P(Blue, Blue) =
c)
P(Yellow, Not Yellow) =
Ex. 3 Andrew is 55. The probability he will be alive in 10
years is 0.72. Ellen is 35. The probability she will be alive
in 10 years is 0.92.
a) What is the probability they will both be alive in 10
years?
P(Andrew, Ellen) =
b) What is the probability only the woman will be alive in
10 years?
P(Not Andrew, Ellen) =
B. If the events are dependent (outcome of the first event
____________ the probability of the second event), then
P(A and B) =
* P(B|A) is read
Ex. 4 A card is randomly drawn from a standard deck of 52
cards. Then a second card is randomly drawn without
replacing the first card. Find the probability of the
following:
a) the first card is an 8 and the second card is a queen.
P(8, Q) =
*note – in the second probability, an 8 is now missing from the deck,
therefore leaving only ___ cards for the second drawing.
b) both cards are hearts.
P(Heart, Heart) =
*note – in the second probability, a heart is now missing from the deck,
therefore leaving only ___ hearts out of ___ cards for the second
drawing.
Ex. 5 A bag contains 20 marbles: 8 red, 5 blue, 4 green, and
3 yellow. A marble is drawn at random, then a second
marble is drawn without replacing the first. Find the
probability of the following:
a) P(Red, Green) =
b) P(Blue, Blue) =
c)
P(Yellow, not Yellow) =
Ex. 6 The probability that a camera produce is defective is
0.10. In a batch of 100 cameras, what is the probability
that the next two randomly chosen cameras will be
defective?
P(Defective, Defective) =
Assignment w/s Probability #1-6
II.
“Or” Compound Probabilities – The chance of one
event or another happening.
A. If the events are mutually exclusive (____________
__________________________________________), then
P(A or B) =
Ex. 7 A card is randomly drawn from a deck of 52 cards.
Find the probability of drawing the following:
a)
P(King or Jack) =
b)
P(Ace or Face Card) =
B. If the events are not mutually exclusive (_________________
______________________________________), then
P(A or B) =
Ex. 8 A card is randomly drawn from a deck of 52 cards. Find
the probability of drawing the following:
a) P(Queen or Red) =
b) P(Face or Club) =
Ex. 9 A convenience store manager knows from past experience
that 65% of his customers will buy a fountain drink and that
71% will buy a candy bar. He also knows that 87% of those
who buy a fountain drink also buy a candy bar. Find the
following:
a) P(fountain drink and candy bar) =
b) P(fountain drink or candy bar) =
III.
Dice Problems
Ex. 10 When rolling a pair of dice, find the probability for the
following outcomes.
a)
sum of 8. P(8) =
Shortcut for dice probabilities
Dice Total
# of Ways
out of 36
2
3
b)
P(10 or 7) =
c)
P(more than 8) =
4
5
6
7
8
9
10
11
12
Assignment
• Finish Probability worksheet