Please!!
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.
I was the one that answered you before when you had the typo (you had S instead of A for the short-tailed mice)
and I actually found my scrap piece of paper where I made my Venn diagram.
so....
My Venns agree with your data, and
n(M' union S)
= n(non male) + n(short tailed) - n(non-male AND short-tailed) = 22 +18 - 7 = 33
The 5+6 would be the intersection of male and short-tailed,
but we need to subtract the intersection of the non-males and the shorttailed.
The 11 you are talking about would be the males, not the non-males.
(Put your pinkie finger over the circle containing the males.
that leaves you with the 49, including the 2 outside all 3 circles, notice the 11 you are taling about are already excluded.
Now what do you see as mice belonging to both the 22 remaining mice AND the short-tailed mice not covered by your finger?
Isn't that 7 ?
To solve the expression "n(M' U S)" and understand why the answer is 33, let's break down the calculation step by step.
First, let's clarify the notation used:
- M' represents the complement of the set M, which means all the mice that are not male. Since there are 49 mice in total and 27 are male, the number of mice that are not male (M') is 49 - 27 = 22.
- S represents the set of mice with short tails, which is given as 18.
- U represents the union of two sets, which means combining all the elements from both sets without duplicates.
Now let's consider "M' U S," which signifies the union of the set M' (not male) and the set S (short-tailed mice). To find the number of mice in this union, we need to add the number of mice in M' and the number of mice in S, but be careful not to double-count the overlapping region.
From the given information, we know that:
- M' = 22 (not male mice)
- S = 18 (mice with short tails)
Now, let's determine the overlapping region. From your Venn diagram, you mentioned that the overlap between M (male) and D (short-tailed mice) is 5 + 6 = 11. However, we are interested in the mice that are either not male or short-tailed but not both (M' U S), which means we need to subtract the overlapping region.
The number 7 comes from subtracting the overlapping region (11) from the total number of mice that have at least one of the characteristics (either not male or short-tailed), which is given by:
Total = M' + S - Overlap
Total = 22 + 18 - 11
Total = 39 - 11
Total = 28
So, the number of mice in the union M' U S is 28. Therefore, the correct answer to "n(M' U S)" is 28.
Note: In your initial question, you mentioned that the answer provided is 33. However, based on the given information and calculations, the answer should be 28. Please double-check the source of the provided answer or provide additional information if you believe any details are missing.