Take the 2-minute tour ×  The problem I am currently working on
is:  Consider the following information: where    • $A$={Visa
Card}   • $B$={MasterCard} $P(A)=0.5$, $P(B)=0.4$, and $P(A \cap
B) = 0.25$  The part I am having difficulty with is part (e):
Given that an individual is selected at random and that he or
she has at least one card, what is the probability that he or
she has a Visa Card?  For some reason it is just eluding me.
Could someone help me?  share|improve this question Do you
understand how to calculate conditional probability in general?
–  Ben Millwood Feb 25 '13 at 0:42 add comment  2 Answers  up
vote 2 down vote accepted  The probability of having at least
one card is: $$P(A)+P(B)-P(A\cap B) = 0.65 $$  Denote C={at
least one card).  The probability you need (definition of
conditional probability):  $$ P(A\;|\;C) = \frac {P(A\cap
C)}{P(C)}$$  If you have a Visa card, you have at least one
card, so $P(A\cap C)=P(A)$  $$ P(A\;|\;C) = \frac {P(A)}{P(C)} =
\frac{0.5}{0.65}$$  share|improve thi