MATH 55(31) WD SMITH HOMEWORK #7 answers
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Max possible score = 90 (10 pts per problem)

7E #13
10C6 = 210

7E #15
12C4 = 495

7E #21
since 84 = 9C3, Luigi's has 9 toppings.
since 45 = 10C2 Ramona's has 10 toppings.

7A #1a
8 colors * 3 styles  = 24 combinations

7A #1c
8 colors * 4 patterns  = 32 combinations

7A #8
prob(blue) = 15/(10+15+20) = 1/3

7A #11
Empirical probability = 12/30 =2/5 = 0.4 
since 12 correct out of 30 tries (so far)

7A #21
  Prob(do NOT get sum of 7 with 2 fair dice) 
= 1 - prob(DO get sum of 7) 
         6
= 1 - -------- = 5/6 = .83333
        36
Why the 6/36? 
Because 6*6=36 ways to roll 2 dice, but only these 6:
   1+6, 2+5, 3+4, 4+3, 5+2, 6+1
add up to 7.

7A #31
  Odds of getting 1 or 2 when roll a dice
  = Prob(GET 1 or 2) : Prob(get NOT 1 or 2) 
  = 1/3 : 2/3
  = 1:2 odds   (or 1/2).
I.e. if I bet $1 (lose $1 if not 1 or 2), but if I win I get $2 (if is 1 or 2)
then that is a fair bet.

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