At a major track meet, Tara and Emek used recent performance records to estimate their relay team's chance of reaching the final. The data showed probabilities of 0.96, 0.82, and 0.94 for clean first, second, and third baton exchanges. Records also indicated a 0.90 probability that the four runners, as a group, would meet their target running times. Tara and Emek treated the exchange outcomes as approximately independent of one another and, for their model, treated the target-time event as independent of the exchanges. They estimated the probability of meeting all four conditions as 0.96 times 0.82 times 0.94 times 0.90, or about 0.666. Then they examined which factor offered the greatest opportunity for improvement. The second exchange had the lowest success probability at 0.82. If practice raised it to 0.90 while the other probabilities stayed unchanged, the model predicted an overall success probability of about 0.731. Tara cautioned that the independence assumptions were approximations, but the comparison still identified a clear weakness. The team devoted its final practice to the second baton exchange.




