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pleas OIS business statistics 2340 chapter 5 A stock portfolio contains 20 stock

ID: 385931 • Letter: P

Question

pleas OIS business statistics 2340 chapter 5

A stock portfolio contains 20 stocks. Of these stocks, 10 are considered "large-cap" stocks, 5 are "mid-cap," and 5 are "small cap." The portfolio manager has been asked by his client to develop a report that highlights 7 randomly selected stocks. When she presents her report to the client, all 7 of the stocks are large-cap stocks. The client is very suspicious that the manager has not randomly selected the stocks. She believes that the chances of all 7 of the stocks being large cap must be very low. Compute the probability of all 7 being large cap.

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Explanation / Answer

To be calculated: Probability of all 7 large cap stocks

Given values:

Total Number of stocks = 20

Large cap stocks = 10

Mid cap stocks = 5

Small cap stocks = 5

Solution:

The probability of all 7 stocks to be large cap stocks is calculated as below,

Probability of 1st stock to be a large cap = Number of large cap stocks / Total stocks = 10 / 20

Probability of 2nd stock to be a large cap = Remaining large cap stocks / Remaining stocks = 9 / 19

Probability of 3rd stock to be a large cap = Remaining large cap stocks / Remaining stocks = 8 / 18

Probability of 4th stock to be a large cap = Remaining large cap stocks / Remaining stocks = 7 / 17

Probability of 5th stock to be a large cap = Remaining large cap stocks / Remaining stocks = 6 / 16

Probability of 6th stock to be a large cap = Remaining large cap stocks / Remaining stocks = 5 / 15

Probability of 7th stock to be a large cap = Remaining large cap stocks / Remaining stocks = 4 / 14

Probability of all 7 large cap stocks = (10/20) x (9/19) x (8/18) x (7/17) x (6/16) x (5/15) x (4/14)

Probability of all 7 large cap stocks = 0.0015