Answers are in bold
4a) 13/49
4b) 32/245
4c) 22/49
4d) 37/49
4e) 213/245
5) 0 and 1
6) They must sum to 1
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Explanation:
4a)
Add up all the numbers in the frequency column.
50+65+32+38+60 = 245
Then divide the frequency for ground beef (65) over the total (245)
65/245 = 13/49 is the probability of getting ground beef
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4b)
Divide the frequency for bacon (32) over the total calculated earlier.
The probability of getting bacon is 32/245
The fraction cannot be reduced further since 32 and 245 don't have any factors in common other than 1.
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4c)
50 people bought boneless chicken and 60 bought pork tenderloin.
This sums to 50+60 = 110 people out of the 245
110/245 = 22/49 is the probability of someone getting either boneless chicken or pork tenderloin.
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4d)
60 bought pork tenderloin out of the 245 total. That leaves 245-60 = 185 who did not buy pork tenderloin
185/245 = 37/49 is the probability of someone not getting pork tenderloin.
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4e)
32 people bought bacon out of the 245 people total. This means 245-32 = 213 people did not buy bacon.
The probability of not buying bacon is therefore 213/245. The fraction cannot be reduced further.
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5)
Probabilities must always be between 0 and 1.
0 represents "the event is impossible and will never happen"
1 represents "the event is guaranteed to happen"
In other words, 0 represents a 0% chance of it happening, while 1 represents a 100% chance of it happening.
If x is the probability of some event, then [tex]0 \le x \le 1[/tex]
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6)
The probabilities must sum to 1.
In other words, all the probabilities must add to 1.
Like mentioned earlier, the value 1 in terms of probability represents 100%
It's like adding fractions of a pizza and those fractions must add up to a whole pizza. We cannot add past 100% because this is the highest we can go.
