McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
6. Probabilities of Mutually Exclusive Events
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Exercise 17 Page 930

The sum of the probability of an event and the probability of its complement is 1.

3/4 or about 75 %

Practice makes perfect

We are told that a card is randomly drawn from a standard deck.

Recall that the experimental probability of an event measures the likelihood that the event occurs based on the actual results of an experiment. P(Event)= Number of times the event occurs/Number of times the experiment is done We want to find the probability of selecting a card that is not a diamond. Note that this is the complement of selecting a card that is a diamond. The sum of the probability of an event and the probability of its complement is 1. P(Event)+P(Not event)=1 Let's start by finding the probability of selecting a diamond card, which will be our event. The number of times the event occurs is the number of diamond cards, 13, and the number of times the experiment is done is the total number of cards, 52. P( Diamond)=13/52 l← ← lDiamonds Total cards The experimental probability of selecting a diamond card is 1352. Let's now find the probability of its complement, which is selecting a card that is not a diamond.
P(Diamond)+P(Not diamond)=1
13/52+P(Not diamond)=1
Solve for P(Not diamond)
P(Not diamond)=1-13/52
P(Not diamond)=52/52-13/52
P(Not diamond)=39/52
P(Not diamond)=3/4
Convert to percent
P(Not diamond)=0.75
P(Not diamond)=75 %
We found that P(Not diamond) is 34, which can be also written as 75 %.