Probability of Independent Events

M8D3. Students will use the basic laws of probability

M8D2. Students will determine the number of outcomes related to a given event.

•B. Apply the multiplication principle of counting.

Probability(P) is the way to measure the likelihood that an event will occur.

Probability can be expressed as a ratio, decimal or percent.

Probability = number of favorable outcomes

number of possible outcomes

Two events are independent events when the outcome of one event has no effect on the outcome of the other event. EXAMPLE

FIRST EVENT: Tossing a coin and getting HEADS

SECOND EVENT: Rolling a die and getting a number less than 5

Does how the coin lands determine how the die lands?

No, they are independent of one another!

Let’s investigate how to determine the probability of Independent Events

What is the probability of tossing a coin and getting tails and rolling a die and getting a number less than 5. P(T, # < 5)?

What is P(Tails, a number less than 5)?

P(Tails) = # of favorable outcomes

# of total outcomes=

1

2

P(a number less than 5) = # of favorable outcomes

# of total outcomes=

4 2 2

6 2 3

Now, what?

What is P(T, #<5)?1 2 2 2 1

2 3 6 2 3

How can we determine the probability of independent events?

Yes! To determine the probability of 2 independent events, multiply the probabilities of the two events to get the probability of both events together!!!!

This is called the Multiplication Principle of Counting.

Let’s Practice!

A bag contains 6 white, 3 swirled and 1 black marble. A marble is drawn without looking and returned to the bag. Then a second marble is drawn.

1. What is the probability that both marbles are swirled?

P(swirled, swirled) = 3 3 9

10 10 100

2. What is the probability that the first marble is black and the second marble is white?

P(black, white) = 1 6 6 2 3

x 10 10 100 2 50

Will the multiplication principle work for more than 2 events? Let’s see?

3. What is the probability that the first marble is black, the second marble is white and the third marble is swirled?

P(black, white, swirled) =

1 6 3 18 2 9 x x

10 10 10 1000 2 500

Now, try some by yourself!

Brenda rolls two dice. 4. What is the probability that 4 will

come up on each die?

5. P(2, even)=

6. P(odd, odd)=

7. P(red, 4)=

8. P(even, odd)=

4. P(4,4) = 1:36

5. P(2, even)= 1:12

6. P(odd, odd)=1:4

7. P(red, 4)= 0

8. P(even, odd) = 1:4

Next complete the worksheet that your teacher has for you! Remember to…

SHOW ALL WORK!