SOLUTION: SHOW THAT IF B IS A SUBSET OF A, THEN P(B)<= P(A)

Question 1097303: SHOW THAT IF B IS A SUBSET OF A, THEN P(B)<= P(A)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

U = universal set

Let's say that the universal set U has p items inside it where p is some positive integer

Define positive integers m and n such that

Set A has n items inside it

while set B has m items inside it

Every item inside set B is also found in set A. This makes set B a subset of set A.

The probability of selecting an item from set A is since we have n items from set A and p items from set U.

The probability of selecting an item from set B is since we have m items from set B and p items from set U.

Because , this means that .
We can divide both sides of the first inequality () by p to get the second inquality ().
The inequality sign will not flip because p is a positive number.

So this proves that P(B) <= P(A) is true, since,
P(A) = n/p
P(B) = m/p

RELATED QUESTIONS
show that if a subset b, then c-b subset... (answered by dkppathak)

Hello! Suppose A is a subset of B and that P(A)>0 and P(B)>0. Are A and B... (answered by jim_thompson5910)

If A={4,7,10,13,17 and b={3,5,7,9}, then which of the following statements is false?... (answered by solver91311)

If A is subset of B then how can i prove that power set of A is a subset of B? (answered by fcabanski)

If x+p is a factor of ax*+bx+3, show that... (answered by jim_thompson5910)

Given set A= {m,n,o,p} A. Find a subset B of A B. Find a subset C of B C. Is C a... (answered by solver91311,Edwin McCravy)

Prove that if V and W are two independent events such that V is a subset of W, then... (answered by oscargut)

Prove that for any sets A and B, if A is a subset of B, then Help!... (answered by maamarmath)

Show that P[A+B+C] = P[A] +P[B] +P[C] �P[AB]-P[AC]-P[BC] +P[ABC] (answered by robertb)