M408Name______
Probability
Worksheet 8
A Venn Diagram is made up of two or more circles. It is often used in probability to show relationships between events.
Rectangle ‘S’ represents a sample spaceof possible outcomes.
Circles ‘A’ and ‘B’ each represent specific unique events in the sample space S.
If it is possible for two events A and B to both happen at the same time, then their circles will intersect on a Venn Diagram.
I. Shade the region of the picture corresponding to each listed event.
1.) A2.) B
3.) 4.)
The complement of an event ‘A’ refers to all outcomes that are NOT included in ‘A’.
The notation for complement is . The probability of = 1 – P(A).
Shade the region corresponding to each listed event.
5.) 6.)
7.) 8.)
Let ‘S’ represent rolling a 6-sided die. A and B represent different events. Draw Venn diagrams for each pair of events below.
9.) A = number less than 310.)A = a ‘2’
B = an even numberB = an even number
11.)A = a ‘2’12.)A = a # greater than or equal to ‘1’
B = a ‘3’B = a # less than or equal to ‘6’
13.) In which problem (#9 – 12) are the events mutually exclusive?
II. 80 students were asked if they take Math and History classes. The Venn diagram shows the number of students who took each class. Suppose one student is chosen at random, and answer the questions below.
Students in MathStudents in History
23 14 26
17
13.) P(student takes Math) = 14.) P(student takes History) =
15.) P(student takes Math AND History) = 16.) P(student takes Math OR History) =
17.) What does the ‘17’ represent in the diagram above?
18.) Are the events “taking Math class” and “taking History class” independent? Hint: use the formula for independent events to decide.
III. Students’ records indicate that the probability of passing photography is 0.75, the probability of failing economics is 0.65, and the probability of passing at least one of the two courses is 0.85. Regions A, B, C, and D make up the entire sample space of students taking both classes.
ABCD
Passing PhotographyPassing Economics
19.) Which regions (A,B,C, or D) represent passing both classes?
20.)Which regions represent failing both classes?
21.) Which regions represent passing exactly one class?
22.) P(passing economics) =
23.) P(passing both courses) =
24.) P(failing both courses) =
25.) P(passing exactly one course) =
IV. 100 women who recently gave birth were given a survey with 3 yes/no questions, and the following information was recorded.
The mother… / Number of RespondentsIs over 35 years of age / 27
Just had her first child / 21
Has a career / 42
Is over 35 and just had first child / 17
Has a career and just had first child / 9
Is over 35 and has a career / 16
Is over 35, has a career, and just had first child / 7
Use the Venn Diagram to organize the information.
If a mother from this group is randomly selected, find the probabilities below.
26.) P(replied ‘yes’ to exactly 2 of the 3 questions above)
27.) P(replied ‘yes’ to at least 2 of the 3 questions above)
28.) P(replied ‘yes’ to at least one of the 3 questions above)
29.) P(replied ‘yes’ to none of the 3 questions above)