Verified answer

such questions are best handled with a table. For simplicity, drop the decimal. (dots are to preserve format.)

I am assuming that the "c" in the first problem is a typo.

.......B.... -B

A.... 6.............40

-A..................

,,,,,,,25

NOW, what do you know?? well, you know the total probability is 100. You also know that if "B" is "25", and A intersect B is 6, then B intersect -A (not A) is 19

.......B.... -B

A.... 6.............40

-A....19..............

,,,,,,,25............100

NOW, we can fill in the rest of the table:

.......B...,,, -B

A.... 6......34.....40

-A....19.....41.....60.

,,,,,,,25.... 75....100

NOW, the basic definition of probability is: # desired / # possible. Hence, the probability of B | A

is P (A ∩ B) / P (A) = 6/40

P(A ∩ B | A) = 6/40

note that once you specify a "given", you use THAT value for the denominator. For example, what is the probability of a "2" if you roll a die and the number that comes up is even?

Well, you ignore 1, 3, 5 because you know they did not occur. it is 1/3.

always,

tony