What is
2 answers:
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Explanation:
For a function ...
y = f(x)
the inverse function is ...
x = f(y)
To write that in the form y=f^-1(x), you need to solve for y.
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For your function f(x) = e^x +3 this looks like ...
x = e^y +3
x -3 = e^y . . . . . subtract 3
ln(x -3) = y . . . . . take the natural log
So, we can write ...
f^-1(x) = ln(x -3)
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Attached is a graph of these functions. As you might guess from the interchange of x and y, a function and its inverse are mirror images of each other across the line y=x.
Drawing the tree diagram of the problem, we see that there are 6 branches for drawing from Urn A, and then 4 branches for each of the 6 branches, for drawing from Urn B.
This means that there are 6*4=24 possible outcomes, which could be listed as
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1)... (6, 3), (6, 4)},
where the first coordinates represent drawing from urn A, and the second coordinates, drawing from urn B.
(4, 2) is one of these 24, so the probability is 1/24
remark, this problem could also have been solved by the multiplication principle of the probabilities of separate events, that is 1/6 (probability of drawing 4 from Urn A) times 1/4 (probability of drawing 2 from B) = 1/24
Answer: 1/24
This means that there are 6*4=24 possible outcomes, which could be listed as
{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1)... (6, 3), (6, 4)},
where the first coordinates represent drawing from urn A, and the second coordinates, drawing from urn B.
(4, 2) is one of these 24, so the probability is 1/24
remark, this problem could also have been solved by the multiplication principle of the probabilities of separate events, that is 1/6 (probability of drawing 4 from Urn A) times 1/4 (probability of drawing 2 from B) = 1/24
Answer: 1/24