A financial group offers personal insurance and stock trading brokerage services. In total 10,000 people use their services. The group has 7,000 clients who use the insurance service and 5,000 who use the stock trading brokerage service.
a) If we know that a client uses the stock trading brokerage service then what is the probability that he/she uses the insurance services too?
b)If we know that a client uses the insurance service then what is the probability that he/she uses the stock trading brokerage service too?
c) Is the event that a client uses the insurance service independent from the event that he/she uses the stock trading brokerage service? Explain your answer using the results in parts a) and b).
Thank you for the help, I'm really lost with this one!
EDIT: When trying to answer a) I did: P(I)=0.7, P(S)=0.5, P(InS)=0.35. I then did P(InS)/P(I) to get 0.5, it seems wrong to me since that is the same as P(S).
Your basic mistake was to assume independence at start.
$P(I \cup S) = P(I) + P(S) - P(I \cap S)$
$1 = 0.7 + 0.5 - P(I\cap S)$, so $P(I\cap S) = 0.2$
The rest should easily follow !