Question 36122: explain how to find the probability of independent events.use examples.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Two events are independent if the result of one does not affect the other.
One of the best examples I can think of is the event that "it is raining in Boston" is probably independent of the event "it is raining in Los Angeles". In other words the weather in Boston is independent of the weather in LA. However, the weather in San Francisco is NOT independent when compared to the weather in LA, since the cities are so close, that a storm system in California would likely affect the weather in both cities in the same way.
Another independent event would be drawing a card from a deck of cards, replacing the card, and then drawing the second card from the deck. These events, drawing the first card and drawing the second card, are independent, since what happens on the first draw does not affect the outcome of the second draw. However, if you draw a card from a deck and do NOT replace the card, then whatever happened on the first draw DOES affect the result of the second draw. These events are NOT independent.
Other famous examples are the tossing of a coin, which comes up equally heads or tails. If you toss a coin twice or three times or ten times, what happens on the subsequent tosses is INDEPENDENT of the outcomes on the first toss (that is ASSUMING it is a "fair" coin). Now, if the coin toss is performed 10 times, and it comes up heads all 10 times, what would you think about tossing the coin the 11th time? Would you expect it to come up tails because "tails is due"?? The answer is certainly NOT! Assuming that it is a fair coin, you still have a 50-50 chance of getting heads or tails. (If I saw a coin come up heads 10 times in a row, I would be suspicious that it is NOT a fair coin!!) This holds with tossing dice as well.
Now, the way you calculate probabilities of independent events, is you multiply the probability of the first event times the probability of the second event. If you tossed a coin three times, what is the probability of getting three heads? Since the coin tosses are independent, you multiply the probability of getting a head each time (which is 1/2), so this would be 
The basic formula for probability of independent events A and B is
If the events are NOT independent, then we have to recalculate the probability of the second event given that the first event has occurred. Then, we multiply the (Probability of A) times the (Probability of B given that A has already occurred). This is called "conditional probability", which will in all "probability" be your next assignment!!
Hope that helps.
R^2 at SCC
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