Question

Probability and Decision Making in the Congo In his exciting novel Congo, Michael Crichton describes a search by Earth Resources Technology Service (ERTS), a geological survey company, for deposits of boron- coated blue diamonds, diamonds that ERTS believes to be the key to a new generation of optical computers.12 In the novel, ERTS is racing against an international consortium to find the Lost City of Zinj, a city that thrived on diamond mining and existed several thousand years ago (according to African fable), deep in the rain forests of eastern Zaire. After the mysterious destruction of its first expedition, ERTS launches a second expedition under the leadership of Karen Ross, a 24-year-old computer genius who is accompanied by Professor Peter Elliot, an anthropologist; Amy, a talking gorilla; and the famed mercenary and expedition leader, “Captain” Charles Munro. Ross’s efforts to find the city are blocked by the consortium’s offensive actions, by the deadly rain forest, and by hordes of “talking” killer gorillas whose perceived mission is to defend the diamond mines. Ross overcomes these obstacles by using space-age computers to evaluate the probabilities of success for all possible circumstances and all possible actions that the expedition might take. At each stage of the expedition, she is able to quickly evaluate the chances of success. At one stage in the expedition, Ross is informed by her Houston headquarters that their computers estimate that she is 18 hours and 20 minutes behind the competing Euro-Japanese team, instead of 40 hours ahead. She changes plans and decides to have the 12 members of her team—Ross, Elliot, Munro, Amy, and eight native porters—parachute into a volcanic region near the estimated location of Zinj. As Crichton relates, “Ross had double-checked outcome probabilities from the Houston computer, and the results were unequivocal. The probability of a successful jump was .7980, meaning that there was approximately one chance in five that someone would be badly hurt. However, given a successful jump, the probability of expedition success was .9943, making it virtually certain that they would beat the consortium to the site.” Keeping in mind that this is an excerpt from a novel, let us examine the probability, .7980, of a successful jump. If you were one of the 12-member team, what is the probability that you would successfully complete your jump? In other words, if the probability of a successful jump by all 12 team members is .7980.

Question to be answered - • What is the probability that a single member could successfully complete the jump? also complete chart.

Answer 1

SOLUTION:

Let p be the probability that a single member could successfully complete the jump. This probability remains the same for all the n=12 members of the team.

The number of members X out of n=12 who will successfully complete their jumps has a Binomial distribution with success probability (the probability of successfully complete the jump), p

We can the probability the X=x members out of n=12 would successfully complete their jumps as

We know that for X=12, P(X=12) = 0.7980. We need to find p

The probability that a single member could successfully complete the jump is 0.98137