Consider Example 2a, but now suppose that when the key is in a certain pocket, there is a...

Consider Example 2a, but now suppose that when the key is in a certain pocket, there is a 10 percent chance that a search of that pocket will not find the key. Let R and L be, respectively, the events that the key is in the right-hand pocket of the jacket and that it is in the left-hand pocket. Also, let SR be the event that a search of the right-hand jacket pocket will be successful in finding the key, and let UR be the event that a search of the left-hand jacket pocket will be unsuccessful and, thus, not find the key. Find P(SR|UL), the conditional probability that a search of the right-hand pocket will find the key given that a search of the left-hand pocket did not, by

(a) using the identity

determining P(SRUL) by conditioning on whether or not the key is in the right-hand pocket, and determining P(UR) by conditioning on whether or not the key is in the left-hand pocket;

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(b) using the identity