Question

A mineral exploration firm is formed with enough capital to finance 9 ventures.

The probability of any exploration being successful is 0.72. Assume that each exploration is

independent of the others. What are the firm's chances of:

a. exactly 3 successful explorations?

b. at least one successful exploration?

c. zero successes in the 9 ventures?

d. If the firm is successful in only 2 of the 9 ventures, what would you conclude about the

veracity of the overall success rate being touted as 0.72?

Answer 1

Let X denotes the number of successful explorations out of randomly selected 9 ventures.

X ~ Binomial(n = 9, p = 0.72)

The probability mass function of X is

a) The probability of exactly 3 successful explorations

b) The probability of at least one successful exploration

c) The probability of zero successes in the 9 ventures

d) sample proportion of successful exploration

Then, assuming the overall success rate as 0.72 may not be appropriate in this case.