# Difficulty in calculating joint probability

I have a table.

           CASH   CREDIT CARD   DEBIT CARD   TOTAL
UNDER 20   0.09          0.03         0.04    0.16
20-100     0.05          0.21         0.18    0.44
OVER 100   0.03          0.23         0.14     0.4

TOTAL      0.17          0.47         0.36       1


The question is: “Find the probability that a debit card purchase was $20 and over”. In working this question, I became confused. I came up with several possible answers. I would like to know which one is right. How do I work out this question? Is the probability: 1.$0.18+0.14=0.32$2.$ \frac{0.18}{0.44} + \frac{0.14}{0.40} = 0.41+0.35= 0.76$3.$ \frac{0.18+0.14}{0.36} = 0.89$4.$ \frac{0.14+0.18}{0.84}= 0.38$• Does anyone know how to add an attachment? I did not see that option. I saw for links but not attachments. The formatting has changed for the table. It's jumbled up now :\ – aboabo Jul 12 '13 at 4:49 • I tried to fix the table, you should avoid tabs. – Gala Jul 12 '13 at 5:45 • Is this a homework question for some university course? Also, please pay attention to spelling and avoid using too many abbreviations. – Gala Jul 12 '13 at 5:47 • thanks for fixing it. It's a past paper exam question. I'm due to write Economic Statistics exams next week. Do you know the answer? – aboabo Jul 12 '13 at 6:44 ## 1 Answer For homework questions, the site's policy is to provide hints rather than complete solution. Here's one: The question suggests a conditional probability (probability of A given B), which can be computed as $$P(A|B) = \frac{P(A \bigcap B)}{P(B)}$$ What's B? What's A? Then, where is$P(B)$in the table (you can read it directly) and what is$P(A \bigcap B)$(you have to compute it). • Ok. Doesn't seem like a conditional probability to me though. – aboabo Jul 12 '13 at 7:20 • Laurans , Conditional probabilities tend to have 'given' as the big clue to the question being one on conditional probability. Even then,I would not know which event is the condition. Eg, the question doesn't say "“Find the probability that a debit card (was used) GIVEN that the purchase was$20 and over” or '“Find the probability that a purchase was $20 and over GIVEN that a debit card purchase was made”. – aboabo Jul 12 '13 at 7:26 • @Laurans ,I tried again but I am still confused. I used the conditional probability. A=debit card purchase, B=$20 and over. P(B|A)=P(A intersect B) / P(A). P(B)=0.44. P(A intersect B) is what I am confused about again. I came here because I am unsure of what to do. I am still unsure. For P(A intersect B), do I take .18+.14=0.32 OR .18/.44 + .14/40 = 0.41+0.35=.76 OR .18/.36+.14/.36= OR .14+.18=.32 therefore, .32/ .36 OR .32/.84 – aboabo Jul 13 '13 at 20:48
• The top part of the equation is the probability of A intersect B. The probability of debit card purchases and $20 and over. HOW do I calculate it? That is all I am asking. This is what has me confused. I am not asking for an answer, just the methodology. – aboabo Jul 13 '13 at 20:51 • @aboabo It would be too easy if you just needed to look for the word “given” without trying to understand the problem. In your case, wouldn't the sentence imply that you know the purchase was made with a debit card and you want to know the probability that it was under 20$? What are A and B in “A given B” then? – Gala Jul 14 '13 at 18:55