A test was given to a group of students. The grades and gender are summarized below
A B C Total
Male 7 14 11 32
Female 15 13 16 44
Total 22 27 27 76
If one student is chosen at random from those who took the test,
Find the probability that the student was male GIVEN they got a 'C
P(M/C)=11/27=0.4074=40.74
when I tried doing a question like this I got it wrong you need to look back over your work.
To find the probability of a randomly chosen student being male given that they got a 'C', we need to calculate the probability of a student being male and getting a 'C' out of the total number of students who got a 'C'.
Given the table, we can see that a total of 27 students got a 'C', out of which 11 were male. Therefore:
P(M/C) = (Number of male students who got a 'C') / (Total number of students who got a 'C')
P(M/C) = 11 / 27
Approximating the decimal value, we get:
P(M/C) ≈ 0.4074
Converting to a percentage:
P(M/C) ≈ 40.74%
To find the probability that the student was male given they got a 'C,' we need to use the concept of conditional probability.
Conditional probability is the probability of an event (in this case, the student being male) happening, given that another event (the student getting a 'C') has already occurred.
To calculate the conditional probability, we need the probability of the intersection of the two events (the student being male AND getting a 'C'), divided by the probability of the given event (getting a 'C').
In this case, the probability of the student being male and getting a 'C' is 11, which is the number of males who got a 'C'.
The probability of getting a 'C' is 27, which is the sum of the number of males and females who got a 'C'.
So, P(M/C) = (number of males who got a 'C') / (total number of students who got a 'C') = 11/27 ≈ 0.4074 or 40.74%.
Therefore, the probability that the student chosen at random from those who took the test was male, given they got a 'C,' is approximately 0.4074 or 40.74%.