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In a bookstore, the probability that the customer buys a novel is 0.6, and the probability that the customer buys a non-fiction book is 0.4. Suppose that the probability that the customer buys both is 0.2.
a. and d. In the following Venn diagram below, the blue oval represent customers buying a novel, the red oval represents customer buying non-fiction, and the yellow oval customer who buy compact disks.
b.
P (novel or non-fiction) =
P (Blue
Red) =
P (Blue) +
P (Red) -
P (Blue
Red) = 0.6 + 0.4 - 0.2 = 0.8.
c. The overlapping area of the blue oval and red oval represents the customers buying both a novel and a nonfiction book.
A set of 20 German Shepherd dogs is observed. 12 are male, 8 are female, 10 have some brown coloring, and 5 have some white sections of fur. Answer the following using Venn Diagrams.
Draw a Venn diagram simply showing the sets of male and female dogs.
The Venn diagram below demonstrates the situation of mutually exclusive events where the outcomes are independent events. If a dog cannot be both male and female, then there is no intersection. Being male precludes being female and being female precludes being male: in this case, the characteristic gender is therefore mutually exclusive. A Venn diagram shows this as two sets with no intersection. The intersection is said to be the null set using the mathematical symbol ∅.
Draw a second Venn diagram illustrating that 10 of the male dogs have brown coloring.
The Venn diagram below shows the overlap between male and brown where the number 10 is placed in it. This represents : both male and brown. This is the intersection of these two characteristics. To get the union of Male and Brown, then it is simply the two circled areas minus the overlap. In proper terms, will give us the number of dogs in the union of these two sets. If we did not subtract the intersection, we would have double counted some of the dogs.
Now draw a situation depicting a scenario in which the non-shaded region represents "No white fur and female," or White fur′ Female. the prime above "fur" indicates "not white fur." The prime above a set means not in that set, e.g. means not . Sometimes, the notation used is a line above the letter. For example, = .
We met the addition rule earlier but without the help of Venn diagrams. Venn diagrams help visualize the counting process that is inherent in the calculation of probability. To restate the Addition Rule of Probability:
Remember that probability is simply the proportion of the objects we are interested in relative to the total number of objects. This is why we can see the usefulness of the Venn diagrams. [link] shows how we can use Venn diagrams to count the number of dogs in the union of brown and male by reminding us to subtract the intersection of brown and male. We can see the effect of this directly on probabilities in the addition rule.
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