Compound Event
A compound event in mathematics refers to an event that is formed by combining two or more simple events
A compound event in mathematics refers to an event that is formed by combining two or more simple events. These simple events are independent events, meaning that the outcome of one event does not affect the outcome of the other event.
To understand compound events, let’s consider an example:
Example:
Suppose you have a bag with 5 red and 3 blue balls. You randomly draw two balls from the bag without replacement. What is the probability of getting one red ball and one blue ball?
To solve this problem, we need to break it down into simple events and calculate their probabilities.
Step 1: Calculate the probability of getting a red ball on the first draw.
Out of the total 8 balls, 5 are red. So, the probability of selecting a red ball on the first draw is 5/8.
Step 2: Calculate the probability of getting a blue ball on the second draw.
Since we did not replace the first ball, there are now 4 red balls left in the bag. Out of the total remaining 7 balls, 3 are blue. So, the probability of selecting a blue ball on the second draw is 3/7.
Step 3: Calculate the probability of the compound event.
To calculate the probability of the compound event, we multiply the probabilities of the individual events. So, the probability of getting one red ball and one blue ball is (5/8) * (3/7) = 15/56.
Therefore, the probability of getting one red ball and one blue ball in this scenario is 15/56.
It is important to note that in compound events, the order of events can sometimes make a difference. In this example, we considered the first draw as red and the second draw as blue. If we reversed the order, the probabilities would be different, but the concept remains the same.
I hope this explanation helps you understand compound events. If you have any further questions or need additional explanations, feel free to ask!
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