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Unformatted text preview: Chapter 7.3: Rules of Probability In the last class, we learned two important facts about probability. If E is an event in a uniform sample space S then: P ( E ) 1 AND P ( E ) = n ( E ) n ( S ) Today, we will use these facts to find out some more rules about prob- ability. Suppose E = . Then P ( E ) = n ( ) n ( S ) = n ( S ) = 0. In other words, the probability that the impossible event occurs is always zero. Suppose E = S . Then P ( E ) = n ( S ) n ( S ) = 1. In other words, the proba- bility that the guaranteed event occurs is always one. Recall that with sets, we had a formula for finding n ( A B ). We will now use this formula to find a similar formula for finding P ( A B ). Using what we know so far, we have that: P ( A B ) = n ( A B ) n ( S ) Next, we use our formula for n ( A B ): P ( A B ) = n ( A ) + n ( B )- n ( A B ) n ( S ) Now, we simplify a little bit: P ( A B ) = n ( A ) n ( S ) + n ( B ) n ( S )- ( A B ) n ( S ) Each of these three fractions is a probability. This gives us the follow- ing formula for P ( A B ). For any two events A and B : P ( A B ) = P ( A ) + P ( B )- P ( A B ) 1 Lets use this formula in the following question: Example: Suppose I randomly select one card from a deck of 52 playing cards. What is the probability that the card is a seven or is a diamond (or both)? Let A be the event that the selected card is a seven....
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