Question

Question 2 Investment in new issues (the stock of newly formed companies) can be both suicidal and rewarding. Suppose that of 300 newly formed companies in 2015, only 14 appeared to have outstanding prospects. Suppose that you had selected two of these 300 companies back in 2015. Find the probability that both of your companies had outstanding prospects. [3 marks]

Answer 1

Given that investment in new  issues (the stock of newly formed companies) can be both suicidal and rewarding.

Now it is told that there were 300 newly formed companies in 2015 and out of that 14 appeared to have outstanding prospects.

Therefore probability that a company has outstanding prospects is,

Now we have selected two of these 300 companies back in 2015.

We need to find the probability that both of our companies had outstanding prospects.

Let,

X=Number of companies that had outstanding prospects out of the two selected companies.

Binomial Distribution

A discrete random variable X is said to have a binomial distribution if its probability mass function(PMF) is given by,

where 0<p<1.

Coming back to our problem,

In our problem,

Here we need to find the probability that both of our companies had outstanding prospects.

Hence the probability that both of our companies had outstanding prospects is 0.0022