Question 1204607: The number of people who survived the Titanic based on class and sex is in the table ("Encyclopedia Titanica," 2013). Suppose a person is picked at random from the survivors. Round your answers to four decimals, if necessary.
ass Sex Total
Female Male
1st 134 59 193
2nd 94 25 119
3rd 80 58 138
Total 308 142 450
What is the probability that a survivor was male?
P(male) =
What is the probability that a survivor was in the third class?
P(third class) =
What is the probability that a survivor was a male given that the person was in third class?
P(male|third class) =
What is the probability that a survivor was a male and in the third class?
P(male and third class) =
What is the probability that a survivor was a male or in the third class?
P(male or third class) =
Are the events survivor is a male and survivor is in third class mutually exclusive? Why or why not?
No, male and being in third class are not mutually exclusive, since a survivor cannot be both.
Yes, male and being in third class are mutually exclusive, since a survivor cannot be both.
No, male and being in third class are not mutually exclusive, since a survivor can be both.
Yes, male and being in third class are mutually exclusive, since a survivor can be both.
Are the events survivor is a male and survivor is in third class independent? Why or why not?
No, male and being in third class are not independent, since P(male|third class) ≠ P(male).
Yes, male and being in third class are independent, since P(male|third class) ≠ P(male).
Yes, male and being in third class are independent, since P(male|third class) = P(male).
No, male and being in third class are not independent, since P(male|third class) = P(male).
Answer by math_tutor2020(3817)   (Show Source):
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| Female | Male | Total | | 1st class | 134 | 59 | 193 | | 2nd class | 94 | 25 | 119 | | 3rd class | 80 | 58 | 138 | | Total | 308 | 142 | 450 |
There are 142 males out of 450 survivors.
P(male) = 142/450 = 0.3156 approximately.
There are 138 people in 3rd class out of 450 survivors total.
P(3rd class) = 138/450 = 0.3067 approximately
Of the 138 people in 3rd class, 80 are male
P(male given 3rd class) = 80/138 = 0.5797
Many textbooks use a vertical line to represent the key term "given"
P(A | B) = P(A given B)
I prefer using the word "given" to avoid confusing the vertical bar with perhaps the numeric digit one, the lowercase letter L, or the uppercase letter i.
There are 80 male survivors who are in 3rd class out of 450 total survivors.
P(male and 3rd class) = 80/450 = 0.1778 approximately
Be careful not to mix this up with the previous probability.
Use the inclusion-exclusion principle to compute the following
P(male or 3rd class) = P(male) + P(3rd class) - P(male and 3rd class)
P(male or 3rd class) = (142/450) + (138/450) - (80/450)
P(male or 3rd class) = (142+138-80)/450
P(male or 3rd class) = 200/450
P(male or 3rd class) = 0.4444 approximately.
The events "male" and "3rd class" are NOT mutually exclusive because it is possible for both events to happen at the same time. It's possible for a survivor to be both male and be in 3rd class.
Notice how P(male and 3rd class) is nonzero.
Compare the following probability values
P(male given 3rd class) = 0.5797
P(male) = 0.3156
This leads to P(male given 3rd class) ≠ P(male), which leads us to conclude the events "male" and "3rd class" are NOT independent.
The two events are linked somehow. We consider them dependent.
Having prior knowledge of event "3rd class" changes the probability value of P(male).
Summary- P(male) = 0.3156
- P(3rd class) = 0.3067
- P(male given 3rd class) = 0.5797
- P(male and 3rd class) = 0.1778
- P(male or 3rd class) = 0.4444
- male and 3rd class mutually exclusive? No, male and being in third class are not mutually exclusive, since a survivor can be both.
- male and 3rd class independent? No, male and being in third class are not independent, since P(male given 3rd class) ≠ P(male)
The decimal values are approximate.
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