# 5 Probability - Probability The probability of an event is...

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Probability The probability of an event is its true relative frequency, the proportion of times the event would occur if we repeated the same process over and over again. ! Two events are mutually exclusive if they cannot both be true. ! A B A and B are mutually exclusive

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Mutually exclusive Mutually exclusive Pr( A and B ) = 0 Not mutually exclusive Pr( A and B ) ! 0 Pr( purple AND square ) ! 0 For example Event A: First child is female Event B: Second child is female P(A) = 0.48 P(B) = 0.48 But P( A and B ) ! 0, so these events are NOT mutually exclusive.
Probability distribution A probability distribution describes the true relative frequency of all possible values of a random variable. Probability distribution for the outcome of a roll of a die Number rolled ! Frequency ! Probability distribution for the sum of a roll of two dice Sum of two dice ! Frequency ! The addition principle The addition principle : If two events A and B are mutually exclusive, then Pr[ A OR B ] = Pr[ A ] + Pr[ B ]

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The probability of a range Pr[ Number of boys 6] = Pr[6] + Pr[7] + Pr[8] ....
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