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1. If you flip a fair coin 10 times, what is the probability of

a) getting all tails

Is it 1/1024?

b) getting all heads

Is it 1/1024?

c) getting at least one tails?

Is it 1023/1024?

2. If you roll a pair of fair dice, what is the probability of
a) getting a sum of 1

Is it 0?

b) getting a sum of 5

Is it 1/9?

c)getting a sun of 12

Is it 1/36?

3 answers

1.
a (1/2)^10 = 9.77*10^-4 = .000977
indeed 1/1024

b yes

c yes 1 - 1/1024 = 1023/1024

2.
lay the grid out
x 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
a. yes, no up there :)
b. 5/36
c. yes, lower right :)
2. b is 4/36 = 1/9
you were right (I added in the top label five)
xx 1 2 3 4 5 6
--------------------
1| 2 3 4 5 6 7
2| 3 4 5 6 7 8
3| 4 5 6 7 8 9
4| 5 6 7 8 9 10
5| 6 7 8 9 10 11
6| 7 8 9 10 11 12