1. Probability

2. 13.4 Probability of Compound Events
Probability of Two Independent Events: If two events, A and B, are both independent, then the probability of both events occurring is…
P(A and B) = P(A)*P(B)
Probability of Two Dependent Events: If two events, A and B, are dependent, then the probability of both events occurring is…
P(A and B) = P(A) * P(B following A)

3. 13.4 Probability of Compound Events
Example of Independent Events: What is the probability of rolling a 4 on a die 3 times in a row?
Roll 1
Roll 2
Roll 3
P(4) = 1 6
P(three 4s) =
P(4) *
P(4) *
P(4) =
≈ or 0.423%

4. 13.4 Probability of Compound Events
Example of Dependent Events: What is the probability of drawing 6 hearts from a deck of cards without replacement?
Draw 1
Draw 2
Draw 3
Draw 4
Draw 5
Draw 6
P(six hearts) = * * * * *
8 47 =
≈ or %

5. 13.4 Probability of Compound Events
Example: Suppose the odds of the Sixers beating the Kings in Basketball was 5 : 2. What is the probability of the Sixers beating the Kings 4 times in a row?
𝑃(𝑆𝑖𝑥𝑒𝑟𝑠 𝑤𝑖𝑛) 𝑃(𝐾𝑖𝑛𝑔𝑠 𝑤𝑖𝑛) =
P(Sixers win) = 5 7
Odds = 5 2
Game 1
Game 2
Game 3
Game 4
P(4 wins) = * * *
5 7 =
= .26
≈ 26%

6. 13.4 Probability of Compound Events
Example: A particular bag of marbles contains 4 red, 6 green, 2 blue, and 5 white marbles. What is the probability of picking a red, white, and blue marble, in that order?
Pick 1
Pick 2
Pick 3 *
P(r,w,b) =
P(r,w,b) = *
2 15
≈ .0098
What would the probability be with replacement?
Pick 1
Pick 2
Pick 3
P(r,w,b) = *
P(r,w,b) = *
2 17
≈ .0081

7. 13.4 Probability of Mutually
Exclusive Events and Inclusive Events
Mutually Exclusive Events: If two events, A and B, are mutually exclusive, then that means that if A occurs, than B cannot, and vice versa.
Probability of Mutually Exclusive Events: If two events, A and B, are mutually exclusive, then the probability that either A OR B occurs is…
P(A or B) = P(A) + P(B)

8. 13.4 Probability of Mutually
Exclusive Events and Inclusive Events
Inclusive Events: If two events, A and B, are inclusive, then that means that if A occurs, B could also occur, and vice versa.
Probability of Inclusive Events: If two events, A and B, are inclusive, then the probability that either A or B occurs is…
P(A or B) = P(A) + P(B) – P(A and B)

9. 13.4 Probability of Mutually
Exclusive Events and Inclusive Events
Example: A particular bag of marbles contains 4 red, 6 green, 2 blue, and 5 white marbles. If 3 marbles are picked, what is the probability of picking all reds or all greens?
mutually exclusive event
P(red or greens) = P(red) + P(green)
= ∗ 3 16 ∗ ∗ 5 16 ∗ 4 15
= 𝐶 (4,3) 𝐶 (17,3)
+ 𝐶 (6,3) 𝐶 (17,3) = = =
= .0353
≈ 3.53% =
= .0353
≈ 3.53%

10. 13.4 Probability of Mutually
Exclusive Events and Inclusive Events
Example: Slips of paper numbered 1 to 15 are placed in a box. A slip of paper is drawn at random. What is the probability that the number picked is either a multiple of 5 or an odd number?
inclusive event
P(mult of 5 or odd) = P(mult of 5) + P(odd) – P(5 and odd)
= − 1 15 =
= 2 3
≈ 67%

11. 13.4 Probability of Mutually
Exclusive Events and Inclusive Events
Example: Two cards are picked out of a standard deck. What is the probability of both cards being either face cards or clubs?
inclusive event
P(face or clubs)
= P(face) + P(club)
– P(face and club)
= ∗ 11 51
∗ 12 51
− ∗ 2 51
= − =
= .1063
≈ 10.63%

12. 13.4 Probability of Mutually
Exclusive Events and Inclusive Events
Example: 4 coins are tossed. What is the probability of obtaining 2 heads or 1 tail?
mutually exclusive event
P(2 heads or 1 tail )
= P(2 heads) + P(1 tail)
= 𝐶 (4,2) 𝐶 (4,1) 2 4 = =
= .625
= 62.5%

13. 13.4 Probability of Mutually
Exclusive Events and Inclusive Events
In a particular group of hospital patients, the probability of having high blood pressure is 3 8 , the probability of having arteriosclerosis is , and the probability of having both is
Determine whether the events are mutually exclusive or mutually inclusive.
What is the probability that a patient in this group has either high blood pressure or arteriosclerosis?

14. Probability of Two Independent Events:
P(A and B) = P(A)*P(B)
Probability of Two Dependent Events:
P(A and B) = P(A) * P(B following A)
Probability of Mutually Exclusive Events:
P(A or B) = P(A) + P(B)
Probability of Inclusive Events:
P(A or B) = P(A) + P(B) – P(A and B)