Question 1199785
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Part (a)


32 red + 50 blue = 82 total
P(red) = (number of red)/(number total)
P(red) = (32)/(82)
P(red) = (2*16)/(2*41)
P(red) = 16/41


Answer: <font color=red size=4>16/41</font>


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Part (b)


R = set of red marbles labeled 1 to 32
B = set of blue marbles labeled 1 to 50


R = {1,2,3,...,31,32}
B = {1,2,3,...,49,50}


There are 32/2 = 16 odd values in set R.
There are 50/2 = 25 odd values in set B.
There are 16+25 = 41 odd values total.


41/82 = 1/2 of the values are odd.


Answer: <font color=red size=4>1/2</font>


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Part (c)


The notation n(A) refers to "the number of items inside set A".
Example: A = {4,5,6} leads to n(A) = 3.


n(odd) = number of odd values
n(odd) = 41
This was calculated in part (b)


n(red) = number of red marbles
n(red) = 32


n(red and odd) = 16
This was calculated in part (b)


n(red or odd) = number of red or odd or both
n(red or odd) = n(odd) + n(red) - n(red and odd) 
n(red or odd) = 41 + 32 - 16
n(red or odd) = 57


Phrased another way: There are 32 red + 25 odd blue = 57 marbles that are red or odd or both.


P(red or odd) = n(red or odd)/n(total)
P(red or odd) = 57/82


Answer: <font color=red size=4>57/82</font>


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Part (d)


n(blue) = 50
n(even) = 41
n(blue and even) = 25


n(blue or even) = n(blue) + n(even) - n(blue and even)
n(blue or even) = 50 + 41 - 25
n(blue or even) = 66


Put another way: There are 50 blue + 16 red even = 66 marbles that are blue or even or both


P(blue or even) = n(blue or even)/n(total)
P(blue or even) = 66/82
P(blue or even) = 33/41


Answer: <font color=red size=4>33/41</font>
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