Question

Investment in new issues​ (the stock of newly formed​ companies) can be both suicidal and rewarding. suppose that of 400 newly formed companies in​ 2010, only 11 appeared to have outstanding prospects. suppose that an investor had selected two of these 400 companies back in 2010. find the probability that at least one of the​ investor's companies had outstanding prospects. round to seven decimal places.

Answer 1

To find the probability that at least one of the investor's companies had outstanding prospects out of 400 newly formed companies, we can use the complement rule. The rounded probability is 0.0067747.

Step-by-step explanation:

To find the probability that at least one of the investor's companies had outstanding prospects, we can use the complement rule. The complement of at least one company having outstanding prospects is that none of the companies have outstanding prospects. Since there are 400 companies in total and only 11 have outstanding prospects, the probability that a single company does not have outstanding prospects is 389/400. Therefore, the probability that both companies do not have outstanding prospects is (389/400)^2. The probability that at least one company has outstanding prospects is 1 - (389/400)^2.

Rounding this to seven decimal places, the probability that at least one of the investor's companies had outstanding prospects is 0.0067747.

Answer 2

Answer: 0.0542438

Step-by-step explanation:

Given : The proportion of newly formed companies in​ 2010 appeared to have outstanding prospects :
`p=(11)/(400)=0.0275`

The number of companies selected : n=2

Using the binomial distribution, the probability of getting success in x trials :-

`P(x)=^nC_xp^x(1-p)^(n-x)`, where n is the total number of trials and p is the probability of getting success in each trial.

Then , the probability that at least one of the​ investor's companies had outstanding prospects :-

`P(x\geq1)=1-P(0)=1-^(2)C_0(0.0275)^0(1-0.0275)^2\\\\=1-(0.9725)^2=0.05424375\approx0.0542438`

Hence, the probability that at least one of the​ investor's companies had outstanding prospects = 0.0542438