# Addition rule for "OR" #### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered. #### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals. #### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/1
0/12
##### Examples
###### Lessons
1. Mutually Exclusive VS. Not Mutually Exclusive
Consider the experiment of rolling a die.
1. Event A: an even number is thrown
Event B: an odd number is thrown
i) List the outcomes for:
$\cdot$ event A
$\cdot$ event B
$\cdot$ event A or B
$\cdot$ event A and B
ii) Mark the outcomes on the Venn Diagram. Are events A, B mutually exclusive?
iii) Determine the following probabilities:
$\cdot$ P(A)
$\cdot$ P(B)
$\cdot$ P(A or B)
$\cdot$ P(A and B)
2. Event A: an even number is thrown
Event B: a multiple of three is thrown
i) List the outcomes for:
$\cdot$ event A
$\cdot$ event B
$\cdot$ event A or B
$\cdot$ event A and B
ii) Mark the outcomes on the Venn Diagram. Are events A, B mutually exclusive?
iii) Determine the following probabilities:
$\cdot$ P(A)
$\cdot$ P(B)
$\cdot$ P(A or B)
$\cdot$ P(A and B)
3. Supplementary info on mutually exclusive and addition rule.
2. There are 20 students in a class. 9 students like pizza and 7 students like pasta. Of these students, 3 students like both. Determine the probability that a randomly selected student in the class like pizza or pasta
1. using the formula.
2. using the Venn Diagram.
3. A card is drawn from a standard deck of 52 cards. Determine the probability that:
1. a heart or a spade is drawn.
2. a heart or a face card is drawn.
3. an ace or a face card is drawn.
4. an ace or a spade is drawn.
4. Use the following information to determine whether the events A, B are mutually exclusive.
1. $P(A)=0.5$
$P(B)=0.3$
$P(A\;$or$\;B)=0.7$
2. $P(A)=\frac{2}{3}$
$P(B)=\frac{1}{5}$
$P(A\;$or$\;B)=\frac{13}{15}$
3. $P(A)=\frac{7}{12}$
$P(B)=\frac{5}{13}$
$P(A\;$and$\;B)=0$
###### Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
• #### Easily See Your Progress We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
• #### Make Use of Our Learning Aids   ###### Practice Accuracy

Get quick access to the topic you're currently learning.

See how well your practice sessions are going over time.

Stay on track with our daily recommendations.

• #### Earn Achievements as You Learn   Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
• #### Create and Customize Your Avatar   Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
###### Topic Notes
$\cdot$ P(A or B): probability of event A occurring or event B occurring during a single trial.

$\cdot$ If events A, B are mutually exclusive:
- events A, B have no common outcomes.
- in the Venn Diagram, the circle for A and the circle for B have no area of overlap.
- P(A or B) = P(A) + P(B)

$\cdot$ If events A, B are not mutually exclusive:
- events A, B have common outcomes.
- in the Venn Diagram, the circle for A and the circle for B have an area of overlap representing the event "A and B".
- P(A or B) = P(A) + P(B) – P(A and B)