Introduction
- Studying Mutually exclusive events are essential in probability because they help us analyze different types of real-world situations where outcomes interact in different ways.
- We learn mutually exclusive events in probability to understand situations where two events cannot happen at the same time.
What are Mutually Exclusive Events?
- Mutually exclusive events are events that cannot happen at the same time.
- For example: When you roll an ordinary dice, you cannot get a 3 and an even number at the same time.
- Two events $A$ and $B$ are Mutually exclusive if,
This means there is no overlap between the two events.
- Mathematically,
Steps To Solve The Mutually Exclusive Events
Here are the steps to solve problems in probability:
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- Event A: Rolling a 2.
- Event B: Rolling a 5.
Put the Values in formula,
The Probability of rolling a 2 or a 5 is $\frac{1}{3}$
Final Answer: $\frac{1}{3}$
- Event A: Drawing a red marble
- Event B: Drawing a blue marble
Total marbles: 10 marbles
Put the Values in formula,
The Probability of drawing a Red or Blue marble is $\frac{1}{2}$
Final Answer: $\frac{1}{2}$
- Event A: Drawing a Heart: 13 Hearts
- Event B: Drawing a Club: 13 Clubs
Total cards: 52 cards
Put the Values in formula,
The probability of drawing either a Heart or a Club from a deck is $\frac{1}{2}$
Final Answer: $\frac{1}{2}$
In a class of 30 students, each child likes different subjects, such as:
- 12 students like Math(M)
- 8 students like Science(S)
- 10 students like History(H)
If a student is selected at random, what is the probability that the student likes math or science?
- Event A: Student like Math: 12
- Event B: Student like Science: 8
Total Students: 30
Put the Values in formula,
The probability that a randomly chosen student likes either math or science is $\frac{2}{3}$
Final Answer: $\frac{2}{3}$
A pizza is cut into 8 equal slices:
- 3 slices have cheese topping(C)
- 2 slices have pepperoni topping(P)
- 3 slices have veggie topping(V)
If a person randomly picks one slice, what is the probability that it is cheese or pepperoni?
- Event A: Cheese slices: 3
- Event B: Pepperoni: 2
Total Slices: 8
Put the Values in formula,
The probability of picking a cheese or pepperoni slice is $\frac{5}{8}$
Final Answer: $\frac{5}{8}$
