# Investing in stocks and probability

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?

Gib Z
Homework Helper
Hoping that you mean probability rather than possibility, id say i dont know the answer.

uart
This is called conditional probability. Denote the probability of event A given that event B has already occured 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 probabilty (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 probabilty 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 probabilty.

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

Some good examples would be.

1. Let A be the probabilty that it rains on a certain day in town A and let B be the probabilty that it rains on that same day in town B. If towns A and B are widely geographically seperated then A and B are independant 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 probabilty that a randomly selected student will score in the top 10% of his year and let B denote the probabilty 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 independant hence the conditional probabilites are less then the unconditional probabilities.

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thanks alot