Question 1195976: Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 16 9 19 44
Female 20 6 7 33
Total 36 15 26 77
Write all solutions as a decimals to the fourth. If one student is chosen at random,
Find the probability that the student got a C:
Find the probability that the student was male AND got a "A":
Find the probability that the student was female OR got an "C":
If one student is chosen at random, find the probability that the student got a 'A' GIVEN they are male:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Given Data Table:
| A | B | C | Total | | Male | 16 | 9 | 19 | 44 | | Female | 20 | 6 | 7 | 33 | | Total | 36 | 15 | 26 | 77 |
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Problem: Find the probability that the student got a C
Look at the bottom row labeled "total". We have 26 students who got a C out of 77 students in the group.
Use a calculator to find that
26/77 = 0.33766233766233
This value is approximate
Round this to four decimal places (i.e. nearest ten-thousandth) and you would end up with 0.3377
Answer: 0.3377
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Problem: Find the probability that the student was male AND got a "A"
In the "male" row, and "got an A" column, there are 16 students.
In short, 16 males got an A.
This is out of the 77 total in the bottom right corner.
16/77 = 0.2077922077922 approximately
This rounds to 0.2078
Answer: 0.2078
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Problem: Find the probability that the student was female OR got an "C"
There are 33 female students, 26 students who got a C, and 7 female students who got a C
33+26-7 = 52 students are female, got a C, or both
52/77 = 0.67532467532468 = 0.6753
which is approximate
Answer: 0.6753
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Problem: If one student is chosen at random, find the probability that the student got a 'A' GIVEN they are male
Whenever you see "given", it is often a very important key word in probability questions.
It means that we know 100% that the information provided is correct. This is simply based on the assumption that the speaker is telling the full truth.
This allows us to narrow our focus. The sample space has been reduced.
So we are GIVEN the selected student is male. What this means is that we focus entirely on the male row.
There are 16 males in this row who got an A, out of 44 males total
16/44 = 0.36363636363637
16/44 = 0.3636
Answer: 0.3636
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