relation of conditional probability to independent events
Conditional probability is probability of a second event given a
first event has already occurred. You can't find the probability of drawing two
aces in a row if your first draw is a king. However, if your first draw is an
ace, then you need to look at the deck in a whole new way to determine the
probability of drawing a second ace.
You have two events happening in this scenario. To pull two aces
from the deck, you must consider that pulling a second ace out of the deck is
dependent upon you pulling out that first ace. When you pull the first ace from
the deck, you are leaving only 3 aces and 51 cards left in the deck; therefore,
this would be an example of conditional probability where the first event
influences the probability of the second event. This is conditional probability
with two dependent events.
A dependent event is when one event influences the outcome of
another event in a probability scenario. Since pulling an ace from the deck
changes the number of aces in the deck, this is an example of dependent events
in a conditional probability.
What if you wanted to look at the probability of drawing just
one ace from the deck? In this case, you would only have one event to consider.
This is known as an independent event, which is when the probability of an
event is not affected by a previous event.
You can also have conditional probability with two independent
events. This happens when you have two events that can occur independently. For
example, I might want to know the probability of pulling an ace out of a deck
of cards while my friend pulls a green marble out of a bag of red and green
marbles. The probability of you pulling an ace out of the deck won't influence
the probability that your friend pulls a green marble out of the bag. These two
events have nothing to do with one another, therefore they are independent
events.
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