Table of Content

• What is Probability?
• What is Compound Probability?
• Compound Probability Formulas
• Multiplication Rule
• Addition Rule for Mutually Exclusive Events
• General Addition Rule
• How to Find Compound Probability?
• Compound Probability Example

Related Articles:
Experimental Probability	Chance and Probability
Probability Distribution	Dependent and Independent Events
Union of Sets	Types of Events in Probability

Sample Questions on Compound Probability

Following are some of the questions based on the formulas of Compound Probability:

Question 1: A jar contains 5 red balls and 3 blue balls. If two balls are randomly drawn without replacement, what is the probability of drawing one red ball and one blue ball?

Solution:

First, let’s find the probability of drawing one red ball and one blue ball separately.

Probability of drawing a red ball on the first draw = 5/8

After drawing a red ball, there are 4 red balls left and 3 blue balls remaining, so the probability of drawing a blue ball on the second draw = 3/7

Similarly, probability of drawing a blue ball on the first draw = 3/8

After drawing a blue ball, there are 5 red balls left and 2 blue balls remaining, so the probability of drawing a red ball on the second draw = 5/7

Therefore, the total probability of drawing one red ball and one blue ball

= (5/8) × (3/7) + (3/8) × (5/7)

= 15/56 + 15/56

= 30/56 = 15/28

Question 2: A fair six-sided die is rolled, and a coin is tossed. What is the probability of rolling an even number on the die and getting heads on the coin?

Solution:

Probability of rolling an even number on a fair six-sided die = 3/6 = 1/2

Probability of getting heads on a fair coin toss = 1/2

Since the events are independent, the probability of both events occurring is the product of their individual probabilities.

Therefore,

Total probability = (1/2) × (1/2) = 1/4

Question 3: A bag contains 4 red balls and 5 blue balls. Two balls are drawn randomly with replacement. What is the probability of drawing two blue balls?

Solution:

Probability of drawing a blue ball on the first draw = 5/9

Probability of drawing a blue ball on the second draw (with replacement) = 5/9

Therefore,

Total probability of drawing two blue balls = (5/9) × (5/9) = 25/81

Question 4: A deck of 52 playing cards contains 26 red cards and 26 black cards. If two cards are drawn randomly without replacement, what is the probability of drawing two red cards?

Solution:

Probability of drawing a red card on the first draw = 26/52 = 1/2

After drawing a red card, there are 25 red cards left and 51 cards remaining, so the probability of drawing another red card on the second draw = 25/51

Therefore,

Total probability of drawing two red cards = (1/2) × (25/51) = 25/102

Question 5: An experiment consists of rolling a fair six-sided die and flipping a fair coin. What is the probability of rolling a number less than 4 on the die or getting tails on the coin?

Solution:

Probability of rolling a number less than 4 on a fair six-sided die = 3/6 = 1/2

Probability of getting tails on a fair coin toss = 1/2

Since the events are mutually exclusive, the probability of either event occurring is the sum of their individual probabilities.

Therefore,

Total probability = (1/2) + (1/2) = 1/2

FAQs on Compound Probability

What is compound probability?

Compound probability refers to the likelihood of multiple events occurring together within a single experiment or scenario. It involves analyzing the combined probability of two or more events happening simultaneously or sequentially.

How do you calculate compound probability?

Compound probability is calculated by considering the probabilities of individual events and applying appropriate rules, such as the multiplication rule for independent events or the addition rule for mutually exclusive events.

What are independent events in compound probability?

Independent events are events where the occurrence of one event does not affect the occurrence of another event. In compound probability, if two events are independent, the probability of both events occurring is the product of their individual probabilities.

What are mutually exclusive events in compound probability?

Mutually exclusive events are events that cannot occur simultaneously. In compound probability, if two events are mutually exclusive, the probability of either event occurring is the sum of their individual probabilities.

Why is compound probability important?

Compound probability is important because it allows us to analyze complex scenarios and make informed decisions based on the likelihood of combined events occurring. It is widely used in various fields, including statistics, finance, and engineering, to assess risks, predict outcomes, and solve real-world problems.