How do I find joint probabilities? So I have a chart that lists the probabilities of how much money people paid in a certain store and how they paid. 
                Cash    Credit Card   Debit Card
Less than $20   .09         .03           .04
$20-$100        .05         .21           .18
More than $100  .03         .23           .14

So what is the probability that a credit card purchase was more than $100. I keep thinking you have to add up the probabilities but the answer they give is .49 and I don't know how they got that answer. 
 A: You want to find the conditional probability actually, not the joint distribution:
$\mathbb{P}(\mathrm{Purchase\ was\ more\ than\ $100\ }|\mathrm{\ A\ credit\ card\ was\ used})$.
If you remember the definition of conditional probability, this is just
$\mathbb{P}(\mathrm{Purchase\ was\ more\ than\ $100\ and\ a\ credit\ card\ was\ used}) / \mathbb{P}(\mathrm{\ A\ credit\ card\ was\ used}) $.
To find the probability that a credit card was used, use the Law of Total Probability, i.e. sum up the probabilities of the mutually exclusive events in the second column (where a credit card was used).
A: You need to find the probability that someone paid more than $100 given that they paid with a credit card, i.e.
$$
P(paid\ more\ than\ $100\ |\ paid\ with\ a\ credit\ card) 
$$
Which, by the definition of conditional probability, is equal to
$$
\frac{P(paid\ more\ than\ $100\ and\ paid\ with\ a\ credit\ card)}{P(paid\ with\ a\ credit\ card)}
$$
The probability that someone paid with a credit card shouldn't depend on the amount that they spent, so it should be the sum of all probabilities in the credit card column. The probability that someone paid more than $100 and with a credit card is already give to you. The quantity you're looking for is then
$$
\frac{.23}{.03\ +\ .21+\ .23}=\frac{.23}{.47} \approx .49$$
