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Chapter 4: Problem 111

An investor has the option of investing in three of five recommended stocks. Unknown to her, only two will show a substantial profit within the next 5 years. If she selects the three stocks at random (giving every combination of three stocks an equal chance of selection), what is the probability that she selects the two profitable stocks? What is the probability that she selects only one of the two profitable stocks?

Short Answer

Expert verified
Answer: The probability of selecting the two profitable stocks is 3/10, and the probability of selecting only one of the two profitable stocks is 6/10.

Step by step solution

01

Calculate Total Combinations

To calculate the total number of combinations possible for choosing 3 stocks out of the 5, we will use the combination formula, which is given by C(n, r) = n! / (r!(n-r)!), where n represents the total number of elements and r represents the number of elements chosen at a time. In this case, n = 5 and r = 3. Total Combinations = C(5, 3) = 5! / (3!(5-3)!) Total Combinations = 10
02

Calculate Combinations Including Two Profitable Stocks

To calculate the combinations that include the two profitable stocks, we must consider selecting 2 profitable stocks out of 2, and at the same time 1 non-profitable stock out of 3. Combinations Including Two Profitable Stocks = C(2, 2) * C(3, 1) Combinations Including Two Profitable Stocks = 1 * 3 Combinations Including Two Profitable Stocks = 3
03

Calculate Probability of Selecting Two Profitable Stocks

To calculate the probability of selecting the two profitable stocks, we will divide the number of combinations that include two profitable stocks by the total number of combinations. Probability of Selecting Two Profitable Stocks = Combinations Including Two Profitable Stocks / Total Combinations Probability of Selecting Two Profitable Stocks = 3/10
04

Calculate Combinations Including One Profitable Stock

To calculate the combinations that include only one of the two profitable stocks, we must consider selecting 1 profitable stock out of 2, and at the same time 2 non-profitable stocks out of 3. Combinations Including One Profitable Stock = C(2, 1) * C(3, 2) Combinations Including One Profitable Stock = 2 * 3 Combinations Including One Profitable Stock = 6
05

Calculate Probability of Selecting One Profitable Stock

To calculate the probability of selecting only one of the two profitable stocks, we will divide the number of combinations that include only one profitable stock by the total number of combinations. Probability of Selecting One Profitable Stock = Combinations Including One Profitable Stock / Total Combinations Probability of Selecting One Profitable Stock = 6/10 In conclusion, the probability of selecting the two profitable stocks is 3/10, and the probability of selecting only one of the two profitable stocks is 6/10.

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Most popular questions from this chapter

A sample is selected from one of two populations, \(S_{1}\) and \(S_{2}\), with probabilities \(P\left(S_{1}\right)=.7\) and \(P\left(S_{2}\right)=.3 .\) If the sample has been selected from \(S_{1}\), the probability of observing an event \(A\) is \(P\left(A \mid S_{1}\right)=.2 .\) Similarly, if the sample has been selected from \(S_{2}\), the probability of observing \(A\) is \(P\left(A \mid S_{2}\right)=.3 .\) a. If a sample is randomly selected from one of the two populations, what is the probability that event A occurs? b. If the sample is randomly selected and event \(A\) is observed, what is the probability that the sample was selected from population \(S_{1} ?\) From population \(S_{2} ?\)

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