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Maslowich
3 years ago
11

What is the probability that a randomly selected senator is a Democrat or is up for reelection in November 2014? (Enter your pro

bability as a fraction.)
Mathematics
1 answer:
Vesna [10]3 years ago
3 0

Answer: 20/33

Step-by-step explanation:

According to the table of statistics given for the politicians

number of Dem. Senator = 20

number of Rep. Senator = 13

Total for Senators = 33

Let E be the event,

The required probability is:

P(E) = P(Dem)

= 20/33

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fiasKO [112]

a. The events are mutually exclusive, so

P(A\cup B\cup C)=P(A)+P(B)+P(C)=\boxed{0.9}

b. For the same reason,

P(A\cap B\cap C)=\boxed0

Another way to see this is to use the result from part (a), and the inclusion/exclusion principle:

P(A\cap B\cap C)=P(A)+P(B)+P(C)-P(A\cup B\cup C)

and the right side reduces to 0.

c. Same as (b),

P(A\cap B)=\boxed0

d. Same as (b),

P((A\cup B)\cap C)=\boxed0

We can also use the distributivity rule for unions and intersections to write

P((A\cup B)\cap C)=P((A\cap C)\cup(B\cap C))=P(A\cap C)+P(B\cap C)=0

e. If the A' is the complement of A, then by DeMorgan's law,

P(A'\cap B'\cap C')=P(A\cup B\cup C)'=1-P(A\cup B\cup C)=\boxed{0.1}

4 0
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