Download Section 0.5 Notes

Algebra 2 Honors
Section 0.5 Notes: Adding Probabilities
Probability:
*the likelihood the event will occur.
*must be a number between 0 and 1 inclusive
*Certain to occur: probability of 1.
*Cannot occur: probability of 0.
*Equally likely to occur or not occur: probability of 0.5.
Theoretical Probability
When all outcomes are equally likely that an event will occur is: P(A) =
number of outcomes in A
total number of outcomes
Simply called the probability of an event.
Example 1: A spinner has 8 equal-size sectors numbered from 1 to 8. Find the probability:
a) of spinning a 6.
b) of spinning an even number.
c) of spinning a number greater than 5.
Experimental Probability
This is used when it is impossible or inconvenient to find the theoretical probability. It can be done by performing an experiment,
conducting a survey, or looking at the history of the event.
Example 2: Ninth graders must enroll in one math class. The enrollments of ninth grade students during the previous year are shown
in the bar graph. Find the probability that a randomly chosen student from this year’s 9 th grade class is enrolled in
a) Consumer Math.
100
87
80
69
60
b) Algebra 1 or Intro to Algebra.
51
36
40
20
0
Algebra 1
Consum er
Math
Geom etry
Compound Events
Union: when you consider ALL the outcomes for either of two events A and B. (A, B, A & B)
Intersection: when you consider only the outcomes shared by both A and B. (A & B)
Mutually Exclusive Events: if there is no intersection of A & B (Nothing in common)
IF A & B INTERSECT:
(Since P(A) and P(B) both include P(A & B))
P(A or B) = P(A) + P(B) – P(A & B)
IF A & B ARE MUTUALLY EXCLUSIVE:
P(A or B) = P(A) + P(B)
(do not intersect; have nothing in common, disjoint)
Intro to
Algebra
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B
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A
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UNION of A and B
P(A or B)
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B
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A
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INTERSECTION of A and B
P(A and B)
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B
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INTERSECTION is empty
mutually exclusive events
Example 3: One six-sided die is rolled.
a) What is the probability of rolling a 5 or a multiple of 3?
b) What is the probability of rolling a multiple of 3 or a multiple of 2?
Example 4: In a poll of high school juniors, 6 out of 15 took a French class and 11 out of 15 took a math class. Fourteen out of 15
took French or math. What is the probability that a student took both French and Math?
Example 5: In a survey of 200 pet owners, 103 owned dogs, 88 owned cats, 25 owned birds, and 18 owned reptiles.
a) None of the respondents owned both a cat and a bird. What is the probability that they owned a cat or a bird?
b) Of the respondents, 52 owned both a cat and a dog. What is the probability that a respondent owned a cat or a dog?
c) Of the respondents, 119 owned a dog or a reptile. What is the probability that they owned a dog and a reptile?
Example 6: You put a picture CD that contains 7 pictures in your, computer. You set the options to play the slideshow in a
random order. The computer plays all 7 pictures without repeating any.
a)
Find prob. that the pictures are played in the same order they were put on the disc.
b) You have 3 favorite pictures on the disc. What is the probability that 2 of your favorites play first, in any order?
Example 7: You have an equally likely chance of rolling any value on each of two dice. Find the probability of rolling the given
event.
a) sum of either 4 or 11
b) doubles or a sum of 4
c) 5 on exactly one die
Probability involving Permutations and Combinations
Example 8: Five cards are drawn from a standard 52-card deck. Find each probability
a) Choosing exactly one red card
b) Choosing at least one even numbered card
c) Choosing exactly three black cards
d) That the first 2 cards are red
Example 9: Six marbles are chosen at random from a jar containing 10 green marbles and 7 white marbles. Find the probability of
the following:
a) choosing 7 green marbles
b) choosing 4 green marbles and 2 white marbles
c) choosing exactly one red marble