Understanding Compound Events in Probability: How to Calculate the Likelihood of Multiple Events Happening Together

compound event

A compound event in probability refers to the occurrence of two or more events at the same time

A compound event in probability refers to the occurrence of two or more events at the same time. It involves combining probabilities to determine the likelihood of multiple events happening together. Let’s look at an example to understand it better.

Example:
Suppose we have a bag that contains 5 red marbles, 3 blue marbles, and 2 green marbles. We randomly select two marbles from the bag, one after the other without replacement. We want to determine the probability of getting a red marble followed by a blue marble.

To solve this problem, we need to calculate the probabilities of each event separately and then multiply them together.

Step 1: Calculate the probability of getting a red marble on the first draw.
The total number of marbles in the bag is 5 + 3 + 2 = 10.
The probability of selecting a red marble on the first draw is 5/10 = 1/2, as there are 5 red marbles out of 10 marbles.

Step 2: Calculate the probability of getting a blue marble on the second draw, given that a red marble was selected on the first draw.
After removing one red marble from the bag, there are now 4 red marbles left out of 9 marbles.
The probability of selecting a blue marble on the second draw is 3/9 = 1/3, as there are 3 blue marbles left out of 9 marbles.

Step 3: Multiply the probabilities from Step 1 and Step 2 together.
The probability of getting a red marble followed by a blue marble is (1/2) * (1/3) = 1/6.

Therefore, the probability of selecting a red marble followed by a blue marble from the bag is 1/6.

In summary, a compound event in probability involves calculating the individual probabilities of each event and then multiplying them together to determine the probability of multiple events occurring simultaneously.

More Answers: