Definition: Probability is the likelihood of something occurring. Probability must be between 0 and 1, inclusive. Something with 0 probability means that it can never occur. Something with a probability of 1, or 100%, means it will always occur. To calculate probability, we divide the number of favorable occurrences by the total number of possible occurrences.
When two events are independent to each other, it means that the occurrences of one event does not affect the other event’s probability. For instance, the occurrence of getting a six on a die is independent from drawing an ace from a deck of cards.
In order to find the probability of both independent events occurring together, we multiply the probability of the events together. P(A and B) = P(A) x P(B)
In order to find the probability of one event occurring OR another event occurring (where the events are mutually exclusive), we add the probabilities together. P(A or B) = P(A) + P(B)
Otherwise, P(A or B) = P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Example: A girl flips two different quarters. What is the probability she will get tails on both quarters?
Solution: Here, the two quarters are separate. Getting tails on one quarter will not affect the probability of the other. Therefore the two events are separate.
Since the probability of getting tails on a quarter is 1/2 (since it is either heads or tails) and the probability of getting tails on the other quarter is also 1/2, we can multiply the two probabilities together.
1/2 * 1/2 = 1/4
Visually, we can also identify all the possibilities.
Since there are only four possibilities between the two coins, and only one of the instances has both tails, the probability is 1/4.
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