While on a summer trip, Speedy McBrake was stopped by the police for allegedly driving too fast. The fine for such a mishap is $150. Speedy can either pay this fine, or appeal the speeding ticket in a local court house. His attorney, the esteemed Lionel Hutz, is not overly confident that his client has win the appeal. In fact, he feels the likelihood of successfully appealing the ticket is 25%. Should Speedy lose his appeal, he would be required to pay the original fine plus additional court costs of $350. In the event that Speedy wins the appeal, he is not required to pay any court costs or speeding fines. After researching local laws, Lionel discovered that a person can launch a second appeal (should the first one be rejected). Apparently, judges are a little more lenient on the second appeal. Lionel feels that Speedy has a 40% chance of winning the second appeal. The interesting feature about the second appeal is that if Speedy is victorious, he receives a $1,000 payment (to compensate him for the time and effort involved in the appeal process). Further, he does not need to pay any court costs or speeding tickets. If the second appeal is lost, Speedy must pay an additional $350 in court costs (plus the original fine as well as the court costs from the first appeal). Local laws do not permit a third appeal. Using the given information in the Table A determine the strategy that Speedy should follow maximize his expected gains
Probabilities of winning appeals
1st appeal 0.25
2nd appeal 0.40