Probability and Chance

1
Probability and Chance

• adapted from Cheryl Goodman

2
Probability (P)

• Probability is a measure of how likely it is for
  an event to happen.
• We name a probability with a number from 0 to 1.
• If an event is certain to happen, then the
  probability of the event is 1. P1
• If an event is certain not to happen, then the
  probability of the event is 0. P0

3
Probability

• If it is uncertain whether or not an event will
  happen, then its probability is some fraction
  between 0 and 1 (part whole).
• Part of possible favorable outcomes
• Whole of all possible outcomes

4
1. What is the probability that the spinner will
stop on part A?
A
B
C
D

• What is the probability that the spinner will
  stop on
• An even number?
• An odd number?

3
1
2
A
3. What fraction names the probability that the
spinner will stop in the area marked A?
C
B
5
Probability Questions

• Lawrence is the captain of his track team. The
  team is deciding on a color and all eight members
  wrote their choice down on equal size cards. If
  Lawrence picks one card at random, what is the
  probability that he will pick blue?

blue
blue
green
black
yellow
blue
black
red
6

• Donald is rolling a number cube labeled 1 to 6.
  Which of the following is LEAST LIKELY?
• an even number
• an odd number
• a number greater than 5

7
CHANCEwhat are the odds?

• Chance is how likely it is that something will
  happen. To state a chance, we use a percent or a
  ratio ( part part)

½ Probability
0
1
Equally likely to happen or not to happen
Certain to happen
Certain not to happen
Chance
50 5050
0
100
8
Chance

• When a meteorologist states that the chance of
  rain is 50, the meteorologist is saying that it
  is equally likely to rain or not to rain. If the
  chance of rain rises to 80, it is more likely to
  rain. If the chance drops to 20, then it may
  rain, but it probably will not rain.

9
1
2
1. What is the chance of spinning a number
greater than 1?
4
3

1. What is the chance of spinning a 4?
2. What is the chance that the spinner will stop on
   an odd number?

4
1
2
3
5
4. What is the chance of rolling an even number
with one toss of on number cube?
10
Sample Spaces
A sample set refers to the complete set of all
the possible outcomes
Example Roll a die. What are all the possible
outcomes?
Sample set S S 1,2,3,4,5,6
11
Sample Spaces
Example Toss a coin. What are all the possible
outcomes?
Sample space S S H, T
Toss two coins. What is the sample space? S
HH, HT, TH, TT
12
Events
A set of outcomes is referred to as an event. A
specific outcome (part of the whole) For
example, when rolling a die the outcomes that
are an even number would be referred to as an
event. Event 2,4,6 S 1,2,3,4,5,6 It
is clear that outcomes and events are subsets of
the sample space, S.
13
Events
A set of outcomes is referred to as an event. A
specific outcome (part of the whole) For
example, when rolling a die the outcomes that
are an even number would be referred to as an
event. Event 2,4,6 S 1,2,3,4,5,6 It
is clear that outcomes and events are subsets of
the sample space, S.
14
Sample Space versus Events
We use the symbol omega instead of S
so that we dont get mixed up with
events Events are given a capital letter Ex
1, 2, 3, 4, 5, 6 A 2, 4,
6 The sample space is all the possible outcomes
of rolling a dice The event A is rolling an even
number.
15
Compound Events
Sometimes we are asked to find the probability of
one event OR another Sometimes we are asked to
find the probability of one event AND
another Whats the difference? Example What
is the probability of rolling a 2 OR a 4?
16
Compound Problems Multiple Events
What is the probability of rolling a 2 and a 4
if two die are rolled? S 11, 12,
13,14,15,16, 21,22,23,24,25,26,
31,32,33,34,35,36, 41,42,43,44,45,46,
51,52,53,54,55,56,
61,62,63,64,65,66 Event 2 and 4
24,42 All possible outcomes 36 Possible
outcomes of the stated event 2 Therefore the
probability is 2 out of 36 P 0.056
17
Compound Events
S 1,2,3,4,5,6 Event 2 or 4 There are
2 possible outcomes out of 6 P 2/6 P 0.33
18
(No Transcript)
19
Logical connectors And , Or
When we see the probability of event A and B we
multiply When we see the probability of event A
or B, we add Example We roll a die, what is
the probability of rolling a
3 or a 5? 1/6 1/6 2/6 or 0.33 Example We
roll a die and then roll it again, what is the
probability of rolling a 3 and a 5?
1/6 x 1/6 1/36 (much less likely)
20
Compound Events Independent versus
Dependent Events
Independent if event A does not influence the
probability of event
B Dependent if event A does influence the
probability of event
B Example Event A choose a marble
Event B choose a marble They are
independent if I replace the marble, dependent if
I do not replace the marble
21
Compound Events Independent versus
Dependent Events
Example there are 100 skittles 20 red 20 orange
20 green 20 purple 20 yellow What is the
probability of choosing a red one, eating it and
then choosing a yellow one? Are these events
dependent or independent?
22
Compound Events Independent versus
Dependent Events
Example there are 100 skittles 20 red 20 orange
20 green 20 purple 20 yellow What is the
probability of choosing a red one, eating it and
then choosing a yellow one? P(A) X P(B) 20/100
X 20/99 (remember, I ate one)
23
Compound Events Independent versus
Dependent Events
Example there are 100 skittles 20 red 20 orange
20 green 20 purple 20 yellow What is the
probability of choosing 2 red one (I dont
replace the first obviously) P(A) X P(B)
20/100 X 19/99 (remember, I ate one)
24
Compound Events Independent versus
Dependent Events
Example there are 100 skittles 20 red 20 orange
20 green 20 purple 20 yellow What is the
probability of eating 1 orange, 1 green, 1 purple
and then 1 green?
25
20/100 x 20/99 x 20/98 x 19/97
Get it?
26
Compound Events Independent versus
Dependent Events
Example there are 100 skittles 20 red 20 orange
20 green 20 purple 20 yellow Create your own
question