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A test was given to a group of students. The grades and gender are summarized below
If one student is chosen at random from those who took the test,
Find the probability that the student got a 'C' GIVEN they are female.
The total females is 43, total C's are 19 The total females who have a C is 5 of 19
So my answer is 5/19, is this wrong?
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Sonya N. Giving a test to a group of students, the grades and gender are summarized below If one student is chosen at random, Find the probability that the student got a B: Find the probability that the student was female AND got a "B": 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 was male GIVEN they got a 'A':
A
B
C
Total
Male
17
13
14
44
Female
16
6
4
26
Total
33
19
18
70
1 Expert Answer
Patrick L. answered • 09/21/20
BA in Economics with Statistics Minor
A = grade of "A"
B = grade of "B"
C = grade of "C"
P(B) = 19/70 = 0.2714
The probability that the student got a "B" on the test is 0.2714.
P(Female ∩ B) = 6/70 = 0.08571
The probability that the student is a female and got a "B" on the test is 0.08571
P(Female ∪ C) = P(Female) + P(C) - P(Female ∩ C) = (26/70) + (18/70) - (4/70) = 40/70 = 4/7 = 0.5714
The probability that the student is either a female or got a "C" on the test is 0.5714.
P(Male|A) = P(Male ∩ A) ÷ P(A) = (17/70) / (33/70) = (17/70)*(70/33) = 17/33 = 0.5152
The probability that the student who got a "A" on the test is a male is 0.5152.
We'll use this table (below) to answer the questions
| 15 | 10 | 18 | 43 |
| 8 | 20 | 19 | 47 |
| 23 | 30 | 37 | 90 |
There are 90 students total (see bottom right corner). Out of these 90 students, there are 43 total males (see row 1, last column)
The probability of picking a male is therefore,P(Male) = (number of males)/(number total) = 43/90
The answer for this sub-question is 43/90. This is assuming your teacher wants you to write it in fraction form. If she or he wants you to write it in decimal form, then 43/90 = 0.4778 approximately which converts to 47.78% Answer in fraction form: 43/90 Answer in decimal form: 0.4778 (round this however you are instructed to) Answer in percent form: 47.78% (round this however you are instructed to) ----------------------------------------------------------------------------------------------------------------------------------------------- Question: If one student is chosen at random, Find the probability that the student was male AND got a "B":There are 90 students total (see bottom right corner).
There are 10 males who got a B. Look at the first row (male row) and the second columb (B column).
P(male AND got a B) = (number of males who got a B)/(number total) = (10)/(90) = 1/9
Note: Don't forget to fully reduce any fractions as much as possible. Answer in fraction form: 1/9 Answer in decimal form: 0.1111 (approximate) Answer in percent form: 11.11% (approximate) ----------------------------------------------------------------------------------------------------------------------------------------------- Question: If one student is chosen at random, Find the probability that the student was male OR got an "B": There are 43 males total (row1, total column) and 30 people who got a B (look at the bottom of the B column). So there are 43+30 = 73 people who either are male or got a B. We need to subtract off the 10 males who got B's. Why? Because this will help correct for double-counting. So there are 73-10 = 63 people who got a B, they are male, or they are males who got a B grade. At this point, we are not double counting those 10 males who got B's. There are 90 students total (bottom right hand corner of the table). To summarize so far, we have 63 people we want out of 90. Now we divide the two values (63 over 90) P(male OR got a B) = (number who are male or got a B or both)/(number total) P(male OR got a B) = 63/90 P(male OR got a B) = 7/10 Answer in fraction form: 7/10 Answer in decimal form: 0.70 Answer in percent form: 70% ----------------------------------------------------------------------------------------------------------------------------------------------- Question: If one student is chosen at random, find the probability that the student was male GIVEN they got a 'A' Focus only on the "A" column. Cover up everything else. There are 23 people who got an A. Of those 23 people, there are 15 males. Using a calculator, we can see that 15/23 = 0.6521739 approximately Answer in fraction form: 15/23 Answer in decimal form: 0.6521739 (approximate) Answer in percent form: 65.21739% (approximate)