Question

You have the capital to invest in two of four ventures, each of which requires approximately the same amount of investment capital. Unknown to you, two of the investments will eventually fail and two will be successful. You research the four ventures because you think that your research will increase your probability of a successful choice over a purely random selection, and you eventually decide on two. If you used none of the information generated by your research and selected two ventures at random, what is the probability that you would select at least one successful venture? (Hint: Use S1 and S2 for success on ventures one and two respectively, and F1 and F2 on failures for ventures one and two respectively.)

[NOTE: Round your answer to 3 decimals as needed.]

Answer 1

If we use none of the information generated by our research, we have 2 investments which will succeed and 2 which will fail despite any conditions.

Probability to select at least one successful venture

= N(Ways of selecting 2 successful ventures from the 4 ventures) / Total no. of outcomes of the 4 ventures

* N(Selecting 1 or more ventures from these 2 successful ventures) / Total no. of ways to select 2 out of 4 ventures

= / 2⁴ * ( + ) /

= 6/16 * 3/6

= 3/16 = 0.188