1. 6.4 Find Probabilities of Compound Events

2. Vocabulary Compound event:
Combines 2+ events
Using words and or the word or
Mutually exclusive events: no common outcomes
Overlapping events: 1+ common outcome

3. Vocabulary Continued
Independent events: 1 event has no effect on the other
Color of your teacher’s hair and the grade on a test
Dependent events: 1 event affects the other event
Bad weather and number of automobile accidents
Conditional Probability: the probability that one event will occur because another one occurred

4. Let’s Review
If 1 even occurs m ways & another n ways, then the # of both occurring is m*n.
Multiplication Counting Principle
Addition Counting Principle
If groups formed with nothing in common, total # of possibilities is sum of #’s.
Permutations Formula
nPr =
Combinations Formula
nCr =

5. Probability of mutually exclusive events
If A and B are mutually exclusive, then P(A or B)= P(A) + P(B).
Probability of overlapping events
If A and B are overlapping, then P(A or B) = P(A) + P(B) – P(A and B)
If A and B are independent, then P(A and B)= P(A) * P(B).
Probability of Independent events
Probability of Dependent events
If A and B are dependent, then P(A and B)= P(A) * P(B given A).

6. You roll a number cube. Find the probability that you roll a 2 or an odd number.
SOLUTION
Because 2 is an even number, rolling a 2 and rolling an odd number are mutually exclusive events.
P(2 or odd) = P(2) + P(odd) 6 1 = + 3 4 = 6 = 2 3

7. Find the probability of A or B
You roll a number cube. Find the probability that you roll an even number or a prime number.
SOLUTION
Because 2 is both an even number and a prime number, rolling an even number and rolling a prime number are overlapping events. There are 3 even numbers, 3 prime numbers, and 1 number that is both.
P(even or prime) = P(even) + P(prime) – P(even and prime) 3 6 = + – 1 5 6 =

8. 1. You roll a number cube. Find the probability that
1. You roll a number cube. Find the probability that you roll a 2 or a 5. 1 3
ANSWER
2. You roll a number cube. Find the probability that you roll a number less than 4 or an odd number. 2 3
ANSWER

9. Find the probability of A and B
BUS SCHEDULE
You take a city bus from your neighborhood to a location within walking distance of your school. The express bus arrives at your neighborhood between 7:30 and 7:36. The local bus arrives at your neighborhood between 7:30 and 7:40. You arrive at the bus stop at 7:33. Find the probability that you have missed both the express bus and the local bus.
SOLUTION
The events are independent. The arrival of one bus does not affect the arrival of the other bus.

10. There are 6 minutes when the express bus can arrive
There are 6 minutes when the express bus can arrive. You are not at the bus stop for 3 of those minutes.
There are 10 minutes when the local bus can arrive. You are not at the bus stop for 3 of those minutes.
P(you miss express bus)
P(you miss local bus) 3 6 = 1 2 = = 3 10

11. Find the probability of A and B
Multiply the probabilities of the two events: 3 10 1 2 = 3 20 =
P(you miss both buses)
ANSWER
The probability that you miss the express bus and the local bus is 3 20

12. Find the probability of A and B
PEN COLORS
A box contains 3 blue pens and 5 black pens. You choose one pen at random, do not replace it, then choose a second pen at random. What is the probability that both pens are blue?
SOLUTION
Because you do not replace the first pen, the events are dependent. Before you choose a pen, there are 8 pens, and 3 of them are blue. After you choose a blue pen, there are 7 pens left and 2 of them are blue.
P(blue and then blue) = P(blue) P(blue given blue) 3 8 2 7 = = 6 56 = 3 28

13. 3. MARBLES A bag contains 4 red, 5 green, and 2 blue marbles
3. MARBLES A bag contains 4 red, 5 green, and 2 blue marbles. You randomly draw 2 marbles, one at a time. Find the probability that both are red if:
a. You replace the first marble.
ANSWER 16
121
b. You do not replace the first marble.
ANSWER 6 55