e independent events, mutually exclusive events, and exhaus-

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calculation steps and explanations.

 

According to the Congressional Directory, the age distribution for senators
in the 109th U.S. Congress is as follows.
Age (in years) | Number of senators
Under 50
12
50–59
33
60–69
32
70–79
18
80 and over
Suppose that a senator from the 109th U.S. Congress is selected at random.
Let A be the event the senator is under 50, B the event the senator is in
his or her 50s, C the event the senator is in his or her 60s, D the event the
senator is in his or her 70s, E the event the senator is over 80, and T the
event the senator is under 70.
a. Use the table to find P(T).
b. Express event T in terms of events A, B, and C.
c. Determine P(A), P(B), P(C), P(D), and P(E).
d. Compute P(T), using the addition rule and your answers from parts (b)
and (c). Compare your answer with that in part (a).
e. Identify the independent events, mutually exclusive events, and exhaus-
tive events.
f. Find P(T|B°).
Transcribed Image Text:According to the Congressional Directory, the age distribution for senators in the 109th U.S. Congress is as follows. Age (in years) | Number of senators Under 50 12 50–59 33 60–69 32 70–79 18 80 and over Suppose that a senator from the 109th U.S. Congress is selected at random. Let A be the event the senator is under 50, B the event the senator is in his or her 50s, C the event the senator is in his or her 60s, D the event the senator is in his or her 70s, E the event the senator is over 80, and T the event the senator is under 70. a. Use the table to find P(T). b. Express event T in terms of events A, B, and C. c. Determine P(A), P(B), P(C), P(D), and P(E). d. Compute P(T), using the addition rule and your answers from parts (b) and (c). Compare your answer with that in part (a). e. Identify the independent events, mutually exclusive events, and exhaus- tive events. f. Find P(T|B°).
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