Transcript To calculate the probability of compound, dependent events.

Today’s Lesson:
What:
probability of compound,
dependent events
Why:
To calculate the probability of
compound, dependent events.
Vocabulary:
independent
Two events are ______________________________
when
the outcome of one event does NOT affect the
outcome of the other event.
Two events are ______________________________
when
dependent
the outcome of one event DEPENDS on the
outcome of the other. In other words, the first
event ____________________________
the outcome of
affects
the second event.
Scenario
1. Out of a bag of 20 marbles,
calculating the probability of picking
a red marble, setting it aside, and
picking a green marble.
2. When flipping a coin and rolling a
die, calculating the probability of
getting heads and a 4.
Dependent
or
Independent
?
dependent
independent
3. Out of a bucket of tootsie pops,
calculating the probability of picking
independent
a cherry, putting it back in the
bucket, and then picking an orange.
4. When flipping three coins at once,
calculating the probability of getting
three heads in a row.
independent
5. From a standard deck of cards,
calculating the probability of picking
a red Queen, keeping it, and then
picking a black Jack.
dependent
6. From a standard deck of cards,
calculating the probability of picking
independent
a diamond, replacing the card, and
picking the six of hearts.
Trial without replacement . . .
What if we did a Tootsie Pop pick, but did not put
the tootsie pops back in the bucket??
TRIAL #1: Tootsie Pop Double- Pick
Out of 20 “two-pick” trials, how many times
will a grape AND a cherry get picked? The
first pop will NOT be replaced.
P(grape and cherry)
1) What do we need to
know?
# of grape:___
2
# of cherry:___
5
total # of pops: ___
25
3) Do the experiment (20
trials):
2) Theoretical
Probability:
(what should happen)
𝟐
𝟐𝟓
x
𝟓
𝟐𝟒
=
𝟏𝟎
𝟔𝟎𝟎
or
𝟏
𝟔𝟎
4) Experimental
Probability:
(what actually happened)
Examples:
1) What if we tried to pick two grapes in a row–
without replacing the first grape (use same
numbers from our experiment)??
𝟐
𝟐𝟓
x
𝟏
𝟐𝟒
=
𝟐
𝟔𝟎𝟎
or
𝟏
𝟑𝟎𝟎
Examples continued . . .
2) Without replacing any letters, Jane will pick
two letters from a bag containing the following
choices:
M-A-T-H-I-S-C-O-O-L
Answer the following:
a)
b)
P(vowel, then consonant)
P(M, then C)
𝟏
𝟏𝟎
x
𝟏
𝟗
=
𝟒
𝟏𝟎
𝟏
𝟗𝟎
c)
P(two vowels in a row)
𝟒
𝟏𝟎
x
𝟑
𝟗
=
𝟏𝟐
𝟗𝟎
=
𝟐
𝟏𝟓
x
𝟔
𝟗
=
𝟐𝟒
𝟗𝟎
=
𝟒
𝟏𝟓
d)
P(two consonants in a row)
𝟔
𝟏𝟎
x
𝟓
𝟗
=
𝟑𝟎
𝟗𝟎
=
𝟓
𝟏𝟓
END OF LESSON
The next slides are student copies of the notes for this
lesson. These notes were handed out in class and
filled-in as the lesson progressed.
NOTE: The last slide(s) in any lesson slideshow
(entitled “Practice Work”) represent the homework
assigned for that day.
DATE: ______/_______/_______
NAME: ____________________________
ANSWER SPACE (Place answers to questions 1-4 in the table below):
1.
2.
3.
4.
ANSWER SPACE (Place answers to questions 5-10 in the table below):
5.
6.
7.
8.
9.
10.
NAME:
Math-7 NOTES
What:
Why:
DATE: ______/_______/_______
probability of compound, dependent events
To calculate the probability of compound, dependent events.
Vocabulary:
Two events are ______________________________ when the outcome of one event does NOT
affect the outcome of the other event.
Two events are ______________________________ when the outcome of one event DEPENDS
on the outcome of the other. In other words, the first event ____________________________
the outcome of the second event.
Scenario
1.
Out of a bag of 20 marbles, calculating the probability of
picking a red marble, setting it aside, and picking a green
marble.
2.
When flipping a coin and rolling a die, calculating the
probability of getting heads and a 4.
3.
Out of a bucket of tootsie pops, calculating the probability
of picking a cherry, putting it back in the bucket, and then
picking an orange.
4.
When flipping three coins at once, calculating the
probability of getting three heads in a row.
5.
From a standard deck of cards, calculating the probability
of picking a red Queen, keeping it, and then picking a
black Jack.
6.
From a standard deck of cards, calculating the probability
of picking a diamond, replacing the card, and picking the
six of hearts.
Dependent
or
Independent?
Trial without replacement . . .
What if we did a Tootsie Pop pick, but did not put the tootsie pops back in the bucket??
TRIAL #1: Tootsie Pop Double- Pick
Out of 20 “two-pick” trials, how many times will a grape AND a cherry get
picked? The first pop will NOT be replaced. P(grape and cherry)
1) What do we need to know?
# of grape ____
2) Theoretical Probability:
(what should happen)
# of cherry _____
total # of pops: ___
3) Do the experiment (20 trials):
4) Experimental Probability:
(what actually happened)
Examples:
1) What if we tried to pick two grapes in a row – without replacing the first
grape(using the above numbers for our tootsie pop bucket)??
2) Without replacing any letters, Jane will pick two letters from a bag containing
the following choices:
M-A-T-H-I-S-C-O-O-L
Answer the following:
a)
b)
c)
d)
P(M, then C)
P(vowel, then
consonant)
P(two vowels in a
row)
P(two consonants in a
row)
DATE: ______/_______/_______
NAME: ____________________________
Independent Events:
1.
If there is one Queen of Hearts in a deck of 52 shuffled cards, what is the probability of
drawing the Queen of Hearts, putting it back in the deck (replacing it), shuffling the
deck, and then drawing the same card again?
2.
If there are four kings and four jacks in a deck of 52 cards, what is the probability of
drawing a king, putting it back in the deck (replacing it), shuffling the deck, and then
drawing a jack?
3.
What is the probability of flipping heads on a coin and then flipping tails?
4.
What is the probability of rolling a 3 on a six-sided number cube, and then flipping
heads on a coin?
5.
You have a bag of 10 marbles. Four are red and 6 are blue. What is the probability of
drawing a red marble, putting it back in the bag, and then drawing another red
marble?
Dependent Events:
6.
If there are four kings in a deck of 52 cards, what is the probability of drawing a king,
putting it aside (without replacing), and then drawing another king?
7.
Each letter in the word “MATH” is written on a card and put into a bag. What is the
probability of drawing the “A,” keeping it (not replacing), and then drawing the “H”?
8.
You have a bag of 10 marbles. Four are red and 6 are blue. What is the probability of
drawing a red marble, putting it aside, and then drawing another red marble?
9.
You have a bag of 10 marble. Four are red and 6 are blue. What is the probability of
drawing a blue marble, putting it aside (no replacement), and then drawing a red
marble?
10. In a deck of 52 cards, half are black and half are red. What is the probability of
drawing a black card, putting it aside (without replacing), and then drawing a red
card?
NAME: _______________________________________________________________________________ DATE: ______/_______/_______