Download 8.7 Notes

8.7 – Probability
Probability
 Probability = the likelihood that an event will occur
 Outcomes = possible results of an event
 Probability formula:
 P(event) = # favorable outcomes
# possible outcomes
 All probabilities range from zero (impossible) to one
(guaranteed).
 Ex: Find the probability of rolling 2 dice and receiving a
total of 5.
 There are a total of 6 outcomes on each die, so the total
amount of outcomes for 2 dice is 6•6= 36
 It may help to write outcomes in a sample space…
S  (1,1), (1, 2), (1,3), (1, 4), (1,5), (1,6), (2,1)...(6,6)
 Of those outcomes, how many add to 5?
 (1, 4), (2, 3), (3, 2), (4, 1)
 So the probability is 4/36, which reduces to 1/9
 Ex: In the Illinois Lotto, you pick 6 numbers from 1 to
52. To win, you must have all 6 numbers in any order.
What is the probability of winning the jackpot?
 Since the order of the 6 numbers doesn’t matter, the
number of favorable outcomes (amount of winning
combos)is 1.
 For the total outcomes is a combination, 6 numbers out of
52 are picked, and order doesn’t matter:
 52 
 So the final answer is
   20,358,520
1
20358520
6
Find the probability that the sum of
2 rolled dice is 8.
1. 1/36
2. 1/9
3. ½
4. 5/36
5. 2/9
Find the probability that the sum of
3 rolled dice is 17.
1. 1/72
2. 1/216
3. 17/216
4. 5/216
5. 1/108
In a bag of 3 green marbles, 2 blue marbles, and 5
red marbles, what is the prob. of picking a green
or a blue marble?
1.
2.
3.
4.
5.
1/2
3/50
1/15
3/10
1/3
In a bag of 3 green marbles, 2 blue marbles, and 5
red marbles, what is the prob. of picking a green
or a blue, then a red, without replacement?
1.
2.
3.
4.
5.
1/3
1/24
3/100
1/4
5/18
 If A and B are events in the same sample space, then the
probability of A or B occurring is given by:
P( A  B)  P( A)  P( B)  P( A  B)
 P(A U B) is the probability of A or B occurring and is called A
“union” B

P( A  B) is the probability of A and B occurring
simultaneously and is called A “intersection” B
 Ex: One card is selected randomly from a standard 52-card
deck. What is the probability that it is a heart or a jack?
 There are 13 hearts in a deck and 4 jacks, and 1 jack of hearts
P ( h  J )  P (h)  P ( J )  P ( h  J )
13 4
1
16 4





52 52 52 52 13
 If A represents the desirable outcomes in a sample space,
its complement, or A’, represents the undesirable
outcomes in the sample space.
 P(A’) = 1 – P(A)
 Ex: The probability of Mr. Werner touching the net of a
basketball hoop is 4%. What is the probability that he
doesn’t touch the net?
 100% - 4% = 96%
Find the probability of drawing a
10 or a 6 from a standard deck.
0%
0%
0%
0%
15
/5
2
0%
04
/1
3
5.
07
/5
2
4.
02
/1
3
3.
0.
..
2.
1/169
2/13
7/52
4/13
15/52
0
1.
Find the probability of drawing a
diamond or a non-ace from a
standard deck.
0%
0%
0%
0%
1/
4
0%
0.
..
5.
1
4.
10
/1
3
3.
04
/1
3
2.
49/52
4/13
10/13
15/13
1/4
49
/5
2
1.