Mutually Exclusive Events and Addition Rule

Mutually Exclusive Events and Addition Rule

by Veronica Williams

Mutually Exclusive Events

When two events CANNOT happen at the same time, the events are said to be MUTUALLY EXCLUSIVE.

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An example of this is getting heads on a coin and a tail on the same coin in the same toss.

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Another example would be getting a six on a regular die and a five on the same die in the same roll.

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A pre-Covid example would be being at school and being at home at the same time.

Multiple Choice

If you are picking a card randomly from a deck of cards, the events of picking a jack and picking a heart are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

If you are picking a card randomly from a deck of cards, the events of picking an ace and picking a ‘3’ are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

When rolling a single die, the events of rolling an even number and rolling a ‘5’ are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

When rolling a single die, the events of rolling an odd number and rolling a prime are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

Which of the following pairs of events is mutually exclusive?

• Cards: Ace and Spades

• Two Dice: Odd and Even

• Sit down and stand up

• Sit down and scratch your nose

Multiple Choice

When rolling a single die, the events of rolling an even and an odd number are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

5. Rolling an odd number and rolling an even number on a normal six-sided die are

• Mutually exclusive

• Not mutually exclusive

Multiple Choice

6. Rolling a prime number and rolling an even number on a normal six-sided die are

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

4. If a spinner is numbered 1 – 8, when you spin it the events of spinning an even number and a number less than 4 are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

If a spinner is numbered 1 – 8, when you spin it the events of spinning an even number and a number less than 4 are

Look at the picture to visualize)

• Mutually Exclusive

• Not Mutually Exclusive

If a set of mutually exclusive events covers all possible outcomes then their sum of probabilities is 1.

Example: Arif throws a biased coin. The probability of getting tails is 0.7. Therefore, the probability of getting heads is 1 - 0.7 = 0.3

Multiple Choice

Said throws a biased coin. The probability of getting tails is 0.4.

Work out the probability of getting heads.

• 0.4

• 0.6

• 0.8

• 0.2

Multiple Choice

Laman plants a daffodil bulb. The probability that the bulb will grow is 0.8.

What is the probability that the bulb will not grow?

• 0.8

• 0.2

• 0.6

• 0.4

Multiple Choice

The chance of rolling a 2 is 1/6. What is the chance of not rolling a 2?

• 2/6

• 1/6

• 5/6

• not possible

More complicated OR

• To the right you see cards that can each be described in two ways

• Jack, Queen, King or Ace

• Heart, Club, Diamond or Spade

• So, one card can be two things at once, for example a Queen and a Heart.

When we talk about OR probabilities we have to take "double identity" into account.

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P(Queen or Heart) seems simple... just add the Queen probability to the Heart probability.... BUT

What about the Queen of Hearts? It will get counted twice, so....

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We will have to consider OR and take away AND to get rid of the double count

P(A or B) = P(A) + P(B) - P(A and B)

P(Queen OR Heart) = P(Queen) + P(Heart) - P(Queen of Hearts)

= 4/16 + 4/16 - 1/16

P(Queen or Heart) = 7/16

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​ In this simple example we can count the cards shown to see this is true!

Multiple Choice

If you draw one card from a standard deck, what is the probability of drawing a 5 or a diamond?

• 2/52
• 4/52
• 16/52
• 26/52

Multiple Choice

Which of the following shows how to determine P(shaded number or number less than five)?

• 4/8 + 4/8 - 2/8
• 4/9 + 2/8 - 4/8
• 4/8 + 6/8 + 2/8
• 2/8 + 4/8 - 4/8

Multiple Choice

If you roll one die, what is the probability of getting an even number or a multiple of 3?

(Looking at the picture might help you think about this)

• 1/3

• 2/3

• 1/2

• 1/6

Multiple Choice

The enrollment at Southburg High School is 1400. Suppose 550 students take French, 700 take algebra, and 400 take both French and algebra. What is the probability that a student selected randomly takes French or algebra?

Hint: P(French) + P(Algebra) - P(French and Algebra)

• 1250/1400

• 700/1400

• 550/1400

• 17/28