Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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|cite|improve this question
Do you understand how to calculate conditional probability in general? – Ben Millwood Feb 25 '13 at 0:42
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|cite|improve this answer

Suppose there are $100$ people. How many have a Visa card? how many a Mastercard? how many both? of those who have at least one, how many have a Visa card?

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.