40% received an A in operations; 45% received an A in stats; 20% rec'd an A in both.

abako said:
Hello all,

I am struggling with a problem :(, thanks in advance :rolleyes:

40% of all MBAs received an A in operations, and 45% received an A in statistics. 20% of all MBAs received an A in both classes?

What is the probability that a randomly chosen MBA did not get an A in either of these classes?
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Imagine that there were 100 MBAs. How many of them got an "A" in "operations"? How Many got an "A" in "Statistics"? How many got an A in both? So how many got at least one A? How many did not?
 
Hello both,

Many thanks for helping.

If there are 100 MBA students, the distribution is the following:

A (Operations) = 40
A (Statistics) = 45
A (Both) = 20

If we ignore the people that received an A in both, then it is probable that 85 students received at least one A.

However, we know that 20 of those have received an A in both...so I am wondering if we can we conclude that 65 received an A (some of them one A and some of them two As). If that is correct, then the people who received none is 100-65.

Let me know if I am thinking in the right direction.

Regards,
Alex
 
abako said:
Hello both,

Many thanks for helping.

If there are 100 MBA students, the distribution is the following:

A (Operations) = 40
A (Statistics) = 45
A (Both) = 20

If we ignore the people that received an A in both, then it is probable that 85 students received at least one A.
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Let's not ignore that. Since 40 people got an A in Operations and 20 of them also got an A in Statistics, 40- 20= 20 people got an A in Operations but not in Statistics. Similarly, since 45 people got an A in Statistics and 20 of them also got an A in Operations, 45- 20= 25 people got an A in Statistics but not in Operations.

A total of 20+ 25+ 20= 65 people got an A one or the other or both leaving 100- 65= 35 people who did not.

Another way to calculate how many people got at least one A is 40+ 45- 20= 85- 20= 65. There, after adding the number of people who got an A in Operations and the number of people who got an A in Statistics, we subtract the number of people who got As in both because they have been counted twice.

However, we know that 20 of those have received an A in both...so I am wondering if we can we conclude that 65 received an A (some of them one A and some of them two As). If that is correct, then the people who received none is 100-65.

Let me know if I am thinking in the right direction.

Regards,
Alex
Click to expand...
Yes, that argument is correct. Don't for get that the problem as for a probability not a number of people.
 
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