Adding Probabilities

1
Adding Probabilities

• Lesson 11-3

2
SDAP 3.4

• Understand that the probability of either of two
  disjointed events occurring is the sum of the two
  individual probabilities
• In other words If you are doing an experiment
  and you are looking for one thing OR another to
  happen in a single event, then you figure out the
  probability figuring out how many opportunities
  you have to win over the possible outcomes
  there can be. Sometimes you need to make a
  chart or a Venn diagram to do this because there
  are times when the two choices overlap and you
  cannot count overlapping events twice.

3
Vocabulary

• Mutually Exclusive Events
• Two events that absolutely CANNOT happen at the
  same time.
• Flipping heads AND tails with one coin
• Pulling both a copper coin and a coin with ridges
  out of a bag if you can only pull one coin at a
  time (pennies do not have ridges!)
• Rolling a 5 AND an even number on one die
• NOT Mutually Exclusive
• Two events that can happen at the same time
• Rolling a four AND an even number
• Pulling out a dime or a quarter AND a coin with
  ridges

4
Vocabulary(continued)

• Favorable Outcomes
• Events that could happen so that the probability
  of your event is successful
• Possible Outcomes
• ALL the possible outcomeswhether you want them
  to happen or not

5
The Formula
P

• Number of favorable outcomes

Number of possible outcomes
Probability begins as a fraction, but is
represented as a decimal between zero and one. We
often convert that decimal to a percent.
6
Simple Probability (review)

• Since this type of die has only six sides, the
  total possible outcomes is a 6.
• The total possible outcomes are put in the
  denominator.

7
Simple Probability (review)

• The number of favorable outcomes is equal to the
  amount of even numbers there are one die.
• The favorable outcomes are 2, 4 and 6.
• There are 3 favorable outcomes. This number goes
  in the numerator.

If we divide 1 into 2, the probability of rolling
an even number is 0.5, which is 50.
8
Adding Probabilities

• Look for the keyword OR
• P (even number or 5)
• P (number less than 4 or 6 )
• P (silver coin or penny )
• P (face card or ace)
• Only add probabilities IF the two events are
  mutually exclusive!
• If the events are NOT mutually exclusive, then
  you must look carefully at what is being asked.

9
A Mutually Exclusive Event

• Since all the favorable outcomes, even numbers
  and 5, are mutually exclusive we add them
  together.
• The number of possible outcomes is 6 because
  there are 6 sides on one die.

10
A NOT Mutually Exclusive Event
This 5 belongs to itself AND the odd numbers. We
cannot count it twice!

• Since all the favorable outcomes, odd numbers and
  5, are NOT mutually exclusive we cannot add them
  together.
• The number of possible outcomes is 6 because
  there are 6 sides on one die.

11
A Mutually Exclusive Event

• Since all the favorable outcomes, face cards and
  aces, are mutually exclusive we add them
  together.
• The number of possible outcomes is 52 because
  there are 52 cards in a deck.

12
A NOT Mutually Exclusive Event

• Since all the favorable outcomes, face cards and
  aces, are NOT mutually exclusive we cannot just
  add them together.
• The king of hearts overlaps between the two
  groups. We cannot count that one twice!
• The number of possible outcomes is 52 because
  there are 52 cards in a deck.
• ALWAYS put your fraction in lowest terms!

13
A Mutually Exclusive Event
Coins in the bag 2 pennies, 1 dime, 3 nickels, 5
quarters

• Since all the favorable outcomes, pennies and
  silver coins, are mutually exclusive we add them
  together.
• The number of possible outcomes is 11 because
  there are 11 coins in the bag.

14
A NOT Mutually Exclusive Event
Coins in the bag 2 pennies, 1 dime, 3 nickels, 5
quarters

• Since all the favorable outcomes are NOT mutually
  exclusive we cannot just add them together.
• The pennies overlap between the two groups. We
  cannot count them twice!
• The number of possible outcomes is 11 because
  there are 11 coins in the bag.

15
Your Turn!
If there is nothing in the middle, then the
events are mutually exclusive.

• There are marbles in this bag.
• 4 purple
• 3 blue
• 8 yellow
• P(blue or yellow)_____
• Is it a mutually exclusive event?

YES
16
Your Turn!

• P(6 or number greater than 1)_____
• Is it a mutually exclusive event?

NO
If there is something in the middle, then the
events are NOT mutually exclusive!