Question

On a recent date, a total of 8676 companies were listed with a certain stock exchange. On this day, the probabilities of advancing, declining, and unchange

company stocks appears in the table for the two exchanges. Find the probability the stock was listed on Exchange 1 given that it is advanced.
Probability of
Percentage of Probability of Probability of
Stock Remaining
Stock
Stock
Companies
Listed
Declining
Unchanged
Advancing
0.2646
0.4351
0.6955
0.0399
0.5649
0.2067
0.7524
0.0409
Exchange
Exchange 1
Exchange 2

Answer 1

To find the probability the stock was listed on Exchange 1 given that it is advanced, we can use Bayes' theorem. The probability is 0.2646.

Step-by-step explanation:

To find the probability the stock was listed on Exchange 1 given that it is advanced, we can use Bayes' theorem. Bayes' theorem states that P(A|B) = (P(B|A) imes P(A)) / P(B), where A and B are events. In this case, event A is the stock being listed on Exchange 1 and event B is the stock advancing.

We are given the following information:

• The total number of listed companies = 8676
• P(Advancing) = 0.0399
• P(Exchange 1) = 0.2646

Using Bayes' theorem, we can substitute the values into the formula:

P(Exchange 1|Advancing) = (P(Advancing|Exchange 1) imes P(Exchange 1)) / P(Advancing) = (0.0399 imes 0.2646) / 0.0399 = 0.2646

Therefore, the probability the stock was listed on Exchange 1 given that it is advanced is 0.2646.

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