Compound Probability
Compound probability refers to the likelihood of two or more events occurring together
Compound probability refers to the likelihood of two or more events occurring together. It is used when there is more than one event happening simultaneously or successively, and we want to calculate the probability of both events happening in combination.
To find the compound probability, we multiply the probabilities of each event occurring individually. The formula to calculate compound probability is:
P(A and B) = P(A) * P(B)
where P(A and B) represents the probability of events A and B occurring together, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.
Let’s take an example to understand compound probability better:
Suppose we have a bag with 4 red balls and 6 green balls. We draw two balls from the bag without replacement. We want to find the probability of drawing a red ball followed by a green ball.
Step 1: Calculate the probability of the first event (drawing a red ball). There are a total of 10 balls in the bag, and 4 of them are red. So, the probability of drawing a red ball is P(Red) = 4/10 = 2/5.
Step 2: Calculate the probability of the second event (drawing a green ball after a red ball). Since we are not replacing the first ball, there are now 9 balls left in the bag, with 6 of them being green. So, the probability of drawing a green ball is P(Green) = 6/9 = 2/3.
Step 3: Multiply the individual probabilities to find the compound probability. P(Red and Green) = P(Red) * P(Green) = (2/5) * (2/3) = 4/15.
Therefore, the compound probability of drawing a red ball followed by a green ball is 4/15 or approximately 0.267.
Remember that the events being independent is an important assumption for using compound probability. If the events are dependent, meaning the outcome of one event affects the probability of the other event, the calculations would be different.
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