; Probability and Relative Frequency[1]
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# Probability and Relative Frequency[1]

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```									If a woman were to have a baby in 1990, what is the probability that it would be a boy? # of favorable outcomes Probability = # of possible outcomes 1 = 50 % 2 Probability involves predicting future events. boy P (boy) = = boy or girl

Objective- To differentiate between probability and relative frequency and to solve problems involving both.

Probability involves predicting future events.

Relative Frequency involves data from past even
# of times an event occurred Relative Frequency = # of times it could have occurred

r=

# of boys born in 1990 2,129,000 = total # of births in 1990 4,158,000

 0.512 r  51.2%

Based on relative frequency, the probability of having a boy is actually 51.2%.

In 1990, the state of Illinois tested 3840 skunks for rabies, of which 1446 actually had rabies. What was the relative frequency of skunks with rabies? frequency 1446 r= = 0.377 total opportunities 3840



r

 37.7%

If a hurricane is likely to occur on any day of the week, what is the probability that it will occur on a weekend? # of days in weekend 2 = P (hurricane) = # of days in week 7 2 7



0.286 or 28.6 %

Probability and relative frequency are always expressed as fractions ( or decimals ) between 0 and 1. Probability-future

0  P 1
impossible certain Relative Frequency-past

0  r  1

never occurred

always occurred

Complementary Events
Two events are complementary if their intersection is the empty set and their union is the set of all possible outcomes.
Complementary P(Hurricane on weekend)

2 7

P(Hurricane on weekday)

+

5 7

=

1

The sum of probabilities for complementary events always equals 1. P(It will rain) + P(It will not rain) 30% + 70% = 100%

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