Probability of Compound Events

Probability of Compound Events

By Armathia Sambrano

​Learning Targets:

​-find the probability or intersection of an event.

-apply the concept of probability in solving real life problems.

​At the end of this week, I CAN:

Multiple Choice

The formula to find the probability of Mutually Exclusive events is____.

• $$P(AUB)=P(A)+P(B)$$  

• $$P(AUB)=P(A)xP(B)$$  

• $$P(AUB)=P(A)-P(B)$$  

• $$P\left(A\cap B\right)=\ P\left(A\right)+\ P\left(B\right)$$

Probability of Mutually INCLUSIVE Events

The probability of event A or event B that are inclusive is equal to the probability pf event A plus the probability of event B minus the probability of their intersection.

​

P (A∪B) = P(A) + P(B) - P (A∩B)

​

Mutually inclusive events are events that can occur at the same time in a single trial.

Multiple Select

Identify the mutually inclusive events.

• The probability of selected either a spade or a face card in a deck of 52 cards.

• The probability of drawing a blue marble or a red marble from a jar with 4 red, 8 blue and 7 yellow marbles.

• The probability of selecting a class class president with grades above 90 and a female student.

• The probability of a dice showing a two or a 5

Probability of INDEPENDENT Events

Two events A and B are independent if the occurence of event A DOES NOT affect the occurence of event B.

P(A∩B) = P(A) x P(B)

The probability of two independent events A and B is equal to the product of their individual probabilities P(A) and P(B).

Multiple Select

Which of the following are examples of INDEPENDENT events.

• A coin is tossed and a die is rolled. Find the probability of landing on a tail of the coin and rolling a 4 on the die.

• A bag contains 5 red balls, 4 green balls and 3 blue balls. One ball is taken, then replaced. Then, another ball is taken. Find the probability of choosing a red ball and then a blue ball.

• There are 6 black pens and 8 blue pens in the drawer. If you take a pen without without looking at it and take another without replacing the first, find the probability that you will get 2 black pens.

Probability of DEPENDENT Events

Two events are dependent when the outcome of the first even influences the outcome of the second event. ​

P(⋂B) = P(A) x P(B/A)

The probability of two dependent events A and B with P(A) > 0 and P(B) > 0.

Multiple Choice

Shareen has to select two students from a class of 23 girls and 25 boys. What is the probability that both students chosen are boys?

• $$\frac{2327}{2256}$$  

• $$\frac{25}{94}$$  

• $$\frac{49}{95}$$  

• $$\frac{29}{48}$$  

Multiple Choice

Identify the type of event.

Probability of getting an even number or a 1 in rolling a die.

• Mutually Inclusive

• Mutually Exclusive

• Dependent event

• Independent event

• Compliment of an event

Multiple Choice

Identify the event.

An airline reports that 97% of its flights arrive on time. What is the probability that a flight will be late?

• Mutually exclusive

• Mutually Inclusive

• Independent Event

• Dependent Event

• Compliment of an Event

Multiple Choice

Identify the event.

Probability spinning a prime number or an odd number on a spinner numbered 1 to 8.

• Mutually Inclusive

• Mutually Exclusive

• Independent Event

• Dependent Event

• Compliment of an event