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Both=And

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1 - the probability of it not being successful

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"Go get some milk 'with' eggs."  The word with is implying to get milk and eggs.

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The phrase "given that" establishes dependency.

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when it says given that it is dependent

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this is read as probability B, given A

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P(A and B) = P(A) * P(B)

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P(B/A)=P(AnB)/P(A)

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P(B|A) = P(A and B)/P(A)

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P(B|A) = P(A and B)/P(A)

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P(A and B) = P(A) * P(B)

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The multiplication rule does not handle disjoint (mutually exclusive)

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probability that both A and B occur is equal to the probability the event A occurs

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If events A and B come from the same sample space, the probability that both A and B occur is equal to the probability the event A occurs times the probability that B occurs.

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the probability that both a and b occurred is equal to the probability of a occurring times b

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Has formula both Independent and Dependent

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Has formula both Independent and Dependent

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Deals with independent and dependent.

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-You multiply the probabilities, when multiplying the probability becomes smaller and smaller.

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P(A and B) = P(A) * P(B|A)

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The multiplication rule applies to independent and dependent only. It has nothing to do with mutually exclusive or not mutually exclusive.