Question

Two brothers enter a race with five friends. The racers draw lots to determine their starting positions. What is the probability that the older brother will start in lane 1 with his brother beside him in lane 2? What is the probability that the two brothers will start beside each other in any pair of lanes?

Answer 1

hmm

Answer 2

So for the first one the logic is that there's a 1/7 probability of the older brother being chosen, then a 1/6 probability of the younger brother being chosen. Multiply the probabilities to get the probability of the entire event happening, that they are in lanes 1 and 2.

Answer 3

Then for the second question we get the pairings:

(1,2)(2,3)(3,4)(4,5)(5,6)(6,7).

Then you can use the sample space from the first question as the denominator, as it represents the number of events where 2 people out of 7 have chosen a lane.