Air Canada and United Continental sell seats on each other’s cross-border flights, coordinating fare structures and discounts while competing for passengers. In 2011 they proposed a closer collaboration involving sharing revenue and coordinating schedules on 19 Canada–U.S. routes.

In Canada, deals of this type are evaluated by the Competition Bureau, and if there are objections to its rulings, a final decision is made by the Competition Tribunal. In mid-2011 the Canadian Competition Bureau ruled against the deal on the grounds that it would monopolize 10 key Canada–U.S. routes and significantly reduce competition on nine others, possibly resulting in increased prices. In August 2011, Air Canada objected to the Competition Bureau ruling, saying that its judgment was “fundamentally misconceived” and that the proposed joint venture would result in “substantial gains in efficiency.”

A few days later, WestJet intervened in the case on the side of the Competition Bureau, arguing that the deal between United Continental and Air Canada would prevent it from competing on equal terms on trans-border routes. WestJet has a deal with American Airlines, but that deal is more restrictive than the one proposed between Air Canada and United Continental.

The case then went to the Competition Tribunal for a decision as to whether to allow the collaboration agreement between Air Canada and United Continental.

Put yourself in the position of an investment banker early in 2011, prior to the above events taking place. You know that Air Canada might propose a closer collaboration agreement with United Continental, and you believe this will be profitable for Air Canada. You need to calculate the chance that such a deal will eventually go through. You assess that Air Canada will propose the collaboration agreement with a probability of 0.6. You also know that, if it does, the Competition Bureau might oppose the deal with a probability of 0.8. If that happens, Air Canada might object with a probability of 0.9. And if it does, WestJet could intervene.

You assess the probability of WestJet intervening in the case at 0.75, which you believe will affect the decision of the Competition Tribunal. If WestJet intervenes, you believe that the chance of the Competition Tribunal blocking the deal is 0.85, and that without WestJet it’s 0.7.

What is the probability of a closer collaboration agreement between Air Canada and United Continental? In your answer, (a) draw a probability tree, (b) clearly indicate which probabilities are joint and which are conditional, and (c) show your calculations clearly.