Each of the 30 students in a class is either male or female, and has blonde, brown, or red hair. If one student is to be randomly selected from the class, what is the probability that the student will either be female or have brown hair?
1. The probability that the student will be both female and have brown hair is 0.1
2. The probability that the student will be female minus the probability that the student will have brown hair is 0.25
a) Since the question is about a probability, we can consider 100 students or any other number, 30 is not important.
b) We can ignore that those who don't have brown hair can have either blonde or red hair.
We can work with Venn diagrams or the 2 X 2 table. And for either one, we can consider probabilities or actual number of people. For those who prefer visualizing.
Looking at the complementary probability, we see that in order to answer the question, it is enough to know the probability for MALE and NOT BROWN HAIR.
Or, if we know one of them, we must know the other one as well.
(1) Not sufficient.
We don't know how many male students with brown hair.
(2) Again not sufficient.
We don't know anything about the male students with brown hair.
(1) and (2) together: From the above, we can see that there is no information about the male students, and definitely there might be some of them with brown hair.
PhD in Applied Mathematics
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