T and M are events such that n(U)=30, n(M)=17, n(T)=10, n((TUM)')=5

Question

Draw a Venn diagram to display this information

Hence find P(T and M)
find P((T and not M)given that M)

Answer 1

My Venn consists of two intersecting circles within a rectangle, rectangle is 30

from your data, I let the intersection of M and T be x
Then the part of only M is 17-x, and the part of only T is 10-x
n((TUM)')=5 --> The part outside the two circles but within the rectangle is 5

17-x + x + 10-x + 5 =30
x = 2

Now you know everything.