Investing in stocks and probability

[beanryu]

the possibility of people investing in stock A is 0.40, the possibility of people investing in stock B is 0.15, and the possiblity of people investing in both stock is 0.05.

the question is what is the possibility of people investing in stock A first and will also invest in stock B.

I think the answer is 0.40*(0.05*0.40), because using a venn diagram, I can see that 0.05 is apart of the 0.40 circle. The possibility of people investing in stock A is 40% and 5% of these people, that is (0.05*0.40), will invest in another stock.

Am I right?

Thank you for your comments!

 

[Gib Z]

Hoping that you mean probability rather than possibility, id say i don't know the answer.

 

[uart]

This is called conditional probability. Denote the probability of event A given that event B has already occurred as P(A|B).

Then P(A|B) = P(A and B) / P(B)

So in this case P(B|A) = 0.05/0.4 = 0.125

Note that is is slightly lower than the unconditional probability (0.15) of buying stock B. So in this case a purchase of stock A makes it less likely that you'll purchase stock B. In general with conditional probability the influence of the apriori knowledge (in this case the knowlegde that the person has already bought stock A) may either increase or decrease the other probability.

When the probability of A and B is greater than what it would be if A and B where independent - that is P(A) times P(B) - then it means that the influence of one event is to increase the probability of the other event. Conversely when the probability of A and B is less than P(A) times P(B) then it means that the influence of one event is to decrease the probability of the other event.

Some good examples would be.

1. Let A be the probability that it rains on a certain day in town A and let B be the probability that it rains on that same day in town B. If towns A and B are widely geographically separated then A and B are independent events. If however towns A and B are near by then P(A and B) is greater then P(A) times P(B) and the conditional probabilities are greater than the unconditional probabilies.

2. Let A denote the probability that a randomly selected student will score in the top 10% of his year and let B denote the probability that the same student truants school more 20 days per term. Here you will find that P(A and B) is less than that which would be expected if the events were independent hence the conditional probabilites are less then the unconditional probabilities.

 

[beanryu]

thanks a lot