Ap Statistics Solutions To Packet 6 - Probability The Study Of Randomness Worksheet With Answers Page 21
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216.83 SUICIDES Here is a two-way table of suicides committed in a recent year, classified by gender
of the victim and whether or not a firearm was used:
Male
Female
Total
Firearm
16,381
2,559
18,940
Other
9,034
3,536
12,570
Total
25,415
6,095
31,510
Choose a suicide at random. Find the following probabilities.
18,940
P firearm =
=
(
)
0.6011
(a) P(a firearm was used)
31,510
2,559
P firearm female =
=
(b) P(firearm | female)
(
|
)
0.4199
6,095
2,559
P female and firearm =
=
(c) P(female and firearm)
(
)
0.0812
31,510
16,381
P firearm male =
=
(d) P(firearm | male)
(
|
)
0.6445
25, 415
16,381
P male firearm =
=
(e) P(male | firearm)
(
|
)
0.8649
18,940
6.85 TOSS TWO COINS Independence of events is not always obvious. Toss two balanced coins
independently. The four possible combinations of heads and tails in order each have probability 0.25.
The events
A = head on the first toss
B = both tosses have the same outcome
may seem intuitively related. Show that P(B|A) = P(B), so that A and B are in fact independent.
P(B | A) = P(both tosses have the same outcome | H on first toss) = 1/2 = 0.5.
P(B) = P(both tosses have same outcome) = 2/4 = 0.5.
Since P(B | A) = P(B), events A and B are independent.
21
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