Exercises 33-48 involve probabilities with dependent events. In Exercises 33-36, we return to our box of chocolates. There are 30 chocolates in the box, all identically shaped. Five are filled with coconut, 10 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the | probability of selecting two caramel-filled chocolates in a row.
Exercises 33-48 involve probabilities with dependent events. In Exercises 33-36, we return to our box of chocolates. There are 30 chocolates in the box, all identically shaped. Five are filled with coconut, 10 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the | probability of selecting two caramel-filled chocolates in a row.
Solution Summary: The author explains how to calculate the probability of selecting two caramel-filled chocolates in a row.
Exercises 33-48 involve probabilities with dependent events.
In Exercises 33-36, we return to our box of chocolates. There are 30 chocolates in the box, all identically shaped. Five are filled with coconut, 10 with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the | probability of selecting
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Match the surfaces (a) - (f) below with the contour diagrams (1) - (6) below those.
(a) Surface (a) matches contour 5 V
V
(b) Surface (b) matches contour 2 V
(c) Surface (c) matches contour 1
(d) Surface (d) matches contour 6 V
(e) Surface (e) matches contour 4 V
(f) Surface (f) matches contour 3 V
(4)
(1)
-0.25
(a)
(b)
(c)
(d)
(e)
y
y
2.5
0.5
1.5
1.5
1.5
y
.3
0.25
OC
0.25
-0.25
(2)
X
1.5
ZI
(f)
y
0.01
0.01
(3)
☑
X
0.01
0.01
0.2
0.2
(5)
0 x
0.5
(6)
0.25
X
X
0.25
0.5
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At least one of the answers above is NOT correct.
The figure shows a hill with two paths, A and B.
(a) What is the elevation change along each path? 400
9400
✓ feet
(b) Which path ascends more rapidly? A v
(c) On which path will you probably have a better view of the surrounding
countryside (assuming that trees do not block your view)? A V
(d) Along which path is there more likely to be a stream?
A V
Note: You can earn 50% partial credit for 2-3 correct answers.
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9800'
A
10000
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B
0
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4)
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
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