The letters in the word STATISTICS are printed on identical index cards with one letter per card. The ten cards are then placed in a hat, and one card is randomly chosen (without looking) from the hat. The chance process we are interested in is what letter is on the selected card.   Consider the following events: V: the letter chosen is a vowel. F: the letter chosen falls in the first Are the events V and F independent or not independent? Explain.

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Chapter1: Combinatorial Analysis
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The letters in the word STATISTICS are printed on identical index cards with one letter per card. The ten cards are
then placed in a hat, and one card is randomly chosen (without looking) from the hat. The chance process we are
interested in is what letter is on the selected card. 

 Consider the following events:
V: the letter chosen is a vowel.
F: the letter chosen falls in the first
Are the events V and F independent or not independent? Explain. 

vo
2.
The letters in the word STATISTICS are printed on identical index cards with one letter per card. The ten cards are
then placed in a hat, and one card is randomly chosen (without looking) from the hat. The chance process we are
interested in is what letter is on the selected card.
(a) Make a table that shows the set of outcomes and the probability of each outcome.
Outcome
Probability
P(F) =
S
33/1060
(b) Consider the following events:
V: the letter chosen is a vowel.
F: the letter chosen falls in the first half of the alphabet (that is, between A and M).
{A, 1}
Determine the following probabilities:
2
P(V) =
to t
P(F) = |-
P(V and F) =
P(V or F) =
1-400
TO
to t
1
-12
=
10
10
to otto
11
To t
+
92
3
10
NIO
SIN
T
10
+
112
810
=
=
+2
A
$12
to
I
V=
(
710
to
F={A,1, c)
P(V^F) = {A₁1}
P(VUF) = { A₁F/C]
V po
&
7
J
Transcribed Image Text:vo 2. The letters in the word STATISTICS are printed on identical index cards with one letter per card. The ten cards are then placed in a hat, and one card is randomly chosen (without looking) from the hat. The chance process we are interested in is what letter is on the selected card. (a) Make a table that shows the set of outcomes and the probability of each outcome. Outcome Probability P(F) = S 33/1060 (b) Consider the following events: V: the letter chosen is a vowel. F: the letter chosen falls in the first half of the alphabet (that is, between A and M). {A, 1} Determine the following probabilities: 2 P(V) = to t P(F) = |- P(V and F) = P(V or F) = 1-400 TO to t 1 -12 = 10 10 to otto 11 To t + 92 3 10 NIO SIN T 10 + 112 810 = = +2 A $12 to I V= ( 710 to F={A,1, c) P(V^F) = {A₁1} P(VUF) = { A₁F/C] V po & 7 J
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