Did you mean 3 transportation options?
If he's randomly choosing options, his probability of choosing any single option is ⅓ each trip. The probability of choosing the same mode of transportation both trips is ⅓ x ⅓ = 1/9. However, there are 3 different ways he can choose the same mode of transportation (i.e. bus twice, cab twice, or train twice). This means the probability of using the same mode of transportation triples: 1/9 x 3 = 3/9 = ⅓
Therefore, the probability of him choosing the same mode of transportation twice (regardless of the mode of transportation) is ⅓.
