Dependent events
Events when the one event affects the outcome of the second event
Dependent events are two or more events which are related to each other such that occurrence of one event affects the occurrence and the probability of the other event. In other words, the outcome of a dependent event depends on the outcome of a previous event.
For example, consider a deck of cards with 52 cards. When the first card is drawn, the probability of drawing a heart is 13/52 or 1/4. However, if the first card drawn was a heart and not placed back into the deck, the probability of drawing another heart when the second card is drawn decreases to 12/51 because there are 12 hearts left in the deck and only 51 cards remaining after the first card has been removed.
Another example of dependent events is drawing marbles from a bag. Suppose there are 5 red and 4 blue marbles in a bag. If one marble is drawn and not placed back into bag, the probability of drawing a red marble on the second draw is different depending on whether the first marble was red or blue. If the first marble was red, then there are only 4 red marbles left in the bag and the probability of drawing a red on the second draw is now 4/8 or 1/2. However, if the first marble was blue, then there are still 5 red marbles left in the bag and the probability of drawing a red on the second draw is increased from the original probability of 5/9 to 5/8.
Understanding dependent events is important in many fields such as probability, statistics, and decision-making. It also helps us to make informed decisions based on the probability of the occurrence of an event, especially given prior information about other related events.
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