(a).
To graph : The Venn diagram showing the overlapping sets
Given information :
Graph :
To draw the diagram, start by drawing two overlapping circles and labeling them
Interpretation :
Write in the probability of both events occurring in the area where the circles overlap:
The probability of A alone occurring, substitute
The probability of neither of neither of the events occurring, subtract all the probabilities written in the circles from
Now, write this number outside of the circles and then draw the graph.
(b).
To calculate: The probability that
The probability that
Given information:
Calculation:
To find the probability
(c).
To calculate: The probability that neither
The probability that neither
Given information:
Calculation:
Use the general addition rule for any two events:
Use the complementary rule:
Hence, the probability that neither
(d).
To calculate: The probability that
The probability that
Given information:
Calculation:
To find the probability of neither of the events occurring, subtract all the probabilities written in the circles of the diagram from
Use the complementary rule:
Hence, the probability that
(e).
To calculate: The probability that
The probability that
Given information:
Verify:
We compare
Hence, the events are not independent.
Chapter 10 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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