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.
please show steps with explanation :)
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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.