Ap Statistics Solutions To Packet 6 - Probability The Study Of Randomness Worksheet With Answers Page 4
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21(c) Toss 4 coins.
If four coins are tossed, then there are (2)(2)(2)(2) = 16 possible outcomes,
each of which consists of a string of four letters that may be H’s or T’s. The sample space is
{HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THTH, TTHH, THHT,
HTTT, THTT, TTHT, TTTH, TTTT}.
6.15 LISTING OUTCOMES, II For each of the following, use a tree diagram or the multiplication
principle to determine the number of outcomes in the sample space.
(a) Suppose a county license tag has a four-digit number for identification. If any digit can occupy
10 × 10 × 10 × 10 =
4
any four positions, how many county license tags can you have?
10 = 10,000.
(b) If the county license tags described in (a) do not allow duplicate digits, how many county license
10 × 9 × 8 × 7 = 5,040
tags can you have?
(c) Suppose the country license tags described in (a) can have up to four digits. How many county
license tags will this scheme allow?
There are 10,000 four-digit tags, 1,000 three-digit tags, 100
two-digit tags, and 10 one-digit tags, for a total of 11,110 license tags.
6.17 ROLLING TWO DICE The table below shows the 36 outcomes when we toll two dice.
(a) Another way to summarize these results is to make a table like this. Complete the table below.
Number of ways
Sum
Outcomes
1
2
(1, 1)
2
3
(1, 2) (2, 1)
3
4
(1, 3) (2, 2) (3, 1)
4
5
(1, 4) (2, 3) (3, 2) (4, 1)
5
6
(1, 5) (2, 4) (3, 3) (4, 2) (5, 1)
6
7
(1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)
5
8
(2, 6) (3, 5) (4, 4) (5, 3) (6, 2)
4
9
(3, 6) (4, 5) (5, 4) (6, 3)
3
10
(4, 6) (5, 5) (6, 4)
2
11
(5, 6) (6, 5)
1
12
(6, 6)
4
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