There are 49 mice in a pet shop.

Question

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
A represents short-failed mice

I made a venn diagram but need help on the following:

1. n(M upside down u W)
2. n(M' U S)
3. P( both mice are short-tailed)

My teacher did not go over these notions so it would be helpful if you explain what it means and how you derive the numbers.....

The probability that Kate goes to the cinema is 0.2. If Kate does not go Claire goes. If Kate goes to the cinema the probability that she is late home is 0.3. If Clair goes to the cinema the probability that she is late home is 0.6.

Calculate the probability that

1. Kate goes to the cinema and is not late
2. The person who goes to the cinema arrives home late.

Answer 1

I will assume that you filled in the Venn diagrams correctly
n(M upside down u W) ---> n(M and W) = 14

n(M' U S) ---> n(M' or S)
Since S is the symbol used for the universal set, the count would be 49

P( both mice are short-tailed)
--- where does the "both" come from ???

------------------------------

Prob(kate goes to show) = .2
prob(Claire goes to show) = .8
prob(kate late) = .3 , prob(kate not late) = .7
prob(clair late) = .6 , prob(claire not late) = .4

prob(kate goes to show and it not late)
= .2(.7) = .14

prob(The person who goes to the cinema arrives home late)
= .2(.7) + .8(.4)
= .14 + .32
= .46

Answer 2

+54