I know I posted this already but there is a typo.
There are 49 mice in a pet shop.
30 mice are white.
27 mice are male.
18 mice have short tails.
8 mice are white and have short tails.
11 mice are male and have short tails.
7 mice are male but neither white nor short-tailed.
5 mice have all three characteristics and
2 have none.
Note:
W represents white mice
M represents male mice
S represents short-failed mice
I made a venn diagram but need help on...
n(M' U S)
The answer says 22+18-7=33
I know that M' means 49-27=22 and the union sign means add the 18 short tails but where does 7 come from? I know you have to subtract the overlap but according to my Venn diagram, the overlap between M and D is 5+6=11.
Ah, the world of mice and Venn diagrams! Let me help you make sense of it with a touch of humor.
Well, it seems like those mice are quite complicated creatures with their white fur, male status, and tail lengths. Let me attempt to shed some laughter on this conundrum.
You're absolutely right - M' represents the number of mice that are not male, which is 22. And we want to find the union of M' (not male) and S (short-tailed).
Now imagine those mice having a little shindig and joining forces. But wait! Some of them are already hanging out together and causing a ruckus. Those 7 mice with short tails managed to sneak their way into the "not male" party, even though they didn't receive their official invitations.
So, when we calculate n(M' U S), we add the number of mice that are not male (22) to the number of mice with short tails (18). But since those pesky 7 mice are double-counted, we need to subtract them to avoid any partying confusion.
Therefore, n(M' U S) = 22 + 18 - 7 = 33. Ta-da!
Remember, when it comes to Venn diagram parties, sometimes there are unexpected guests causing mischief. Keep an eye out for those troublemaking mice, and don't forget to have a laugh along the way!
To find the answer to n(M' U S), we need to calculate the number of mice that are either not male or have short tails.
Starting with the information given:
- We know that there are 27 mice that are male (M), so the complement of M (M') would be 49 - 27 = 22 mice.
- We also know that there are 18 mice with short tails (S).
To find the number of mice that are either not male or have short tails (M' U S), we can add the number of mice in M' and the number of mice in S.
So, n(M' U S) = n(M') + n(S) = 22 + 18 = 40.
However, we need to subtract the overlap between mice that are male and have short tails (M ∩ S). This is where the number 7 comes from.
Based on the information given, we know that:
- 8 mice are white and have short tails (W ∩ S).
- 11 mice are male and have short tails (M ∩ S).
- 5 mice have all three characteristics, white, male, and short tails (W ∩ M ∩ S).
So, the overlap between M and S (M ∩ S) would be 11 - 5 = 6 mice.
Subtracting this overlap from the initial result, we have:
n(M' U S) = 40 - 6 = 34.
Therefore, the correct answer should be 34, not 33. It seems like there might be a mistake in the provided answer.