# 7-3 - Chapter 7.3 Rules of Probability • In the last...

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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 Let’s 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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7-3 - Chapter 7.3 Rules of Probability • In the last...

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