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:

Fill in the Blank

The Probability of the Complement of an Event states that:

If E' is the complement of an event E with respect to sample space S, then P(E') is equal to___.

Fill in the Blank

The Probability of Mutually Exclusive Events

This refers to events that ______ occur at the same time in a single trial.

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?

• $$\frac{2327}{2256}$$  

• $$\frac{25}{94}$$  

• $$\frac{49}{95}$$  

• $$\frac{29}{48}$$  

Fill in the Blank

A bag contains 6 red,  5 blue, and 4 yellow balls. 2 balls are drawn, but the first ball is drawn without replacement. Find P (red, then blue)

Fill in the Blank

A box contains 44 red marbles, 33 green marbles and 22 blue marbles.  One marble is removed from the box and then replaced. Another marble is drawn from the box.  What is the probability that the first marble is blue and the second marble is green?

Fill in the Blank

Find the probability of choosing a green marble at random from a bag containing 5 green marbles and 10 red marbles and then flipping a coin and getting tails.

Fill in the Blank

In a deck of 52 cards, what is the probability of drawing a king or a queen?

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