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course Mth 152
10/7 10
Question: `q001. Note that there are 10 questions in this assignment.
List the possible outcomes if a fair coin is flipped 2 times.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
HH, HT, TH and TT
3
Ok
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Question: `q002. List the possible outcomes if a fair coin is flipped 3 times.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
HHH, HHT, HTH, HTT
THH, THT, TTH, TTT
3
Ok
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Question: `q003. List the possible outcomes if a fair coin is flipped 4 times.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT
THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT
3
Ok
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Question: `q004. If a fair coin is flipped 4 times, how many of the outcomes contain exactly two 'heads'?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
C(4, 2) = 6
3
Ok
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Question: `q005. If a fair coin is flipped 7 times, how many of the outcomes contain exactly three 'heads'?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
35 ways to obtain 3 'heads' on 7 flips
3
Ok
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Question: `q006. If we flip a fair coin 6 times, in how many ways can we get no 'heads'?
In how many ways can we get exactly one 'head'?
In how many ways can we get exactly two 'heads'?
In how many ways can we get exactly three 'heads'?
In how many ways can we get exactly four 'heads'?
In how many ways can we get exactly five 'heads'?
In how many ways can we get exactly six 'heads'?
In how many ways can we get exactly seven 'heads'?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
he number of ways to get exactly one 'head' is C(6,1) = 6.
The number of ways to get exactly two 'heads' is C(6,2) = 15.
The number of ways to get exactly three 'heads' is C(6,3) = 20.
The number of ways to get exactly four 'heads' is C(6,4) = 15.
The number of ways to get exactly five 'heads' is C(6,5) = 6.
The number of ways to get exactly six 'heads' is C(6,6) = 1.
These numbers form the n = 6 row of Pascal's Triangle:
1 6 15 20 15 6 1
3
Ok
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Question: `q007. List all the subsets of the set {a, b}.
Then do the same for the set {a,b,c}.
Then do the same for the set {a,b,c,d}.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
{}{ }, {a}, {b}, {a, b}, {c}, {a, c}, {b, c} and {a, b, c}
3
Ok
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Question: `q008. How many subsets would there be of the set {a, b, c, d, e, f, g, h}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 256 subsets of the given set, which has 8 elements
3
Ok
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Question: `q009. How many 4-element subsets would there be of the set {a, b, c, d, e, f, g, h}?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
C(8, 4) = 8 * 7 * 6 * 5 / ( 4 * 3 * 2 * 1) = 70
2
Ok
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Question: `q010. How many subsets of the set {a,b,c,d} contain 4 elements?
How many subsets of the set {a,b,c,d} contain 3 elements?
How many subsets of the set {a,b,c,d} contain 2 elements?
How many subsets of the set {a,b,c,d} contain 1 elements?
How many subsets of the set {a,b,c,d} contain no elements?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
The number of 3-element subsets is C(4,3) = 4.
The number of 2-element subsets is C(4,2) = 6.
The number of 1-element subsets is C(4,1) = 4.
The number of 0-element subsets is C(4,0) = 1.
1
Ok
"
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