James lives in San Francisco and works in Mountain View. In the morning, he has 333 transportation options (bus, cab, or train) to work, and in the evening he has the same 333 choices for his trip home. If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?

Question

Mathematics

Ms. Congeniality

9 July, 23:54

James lives in San Francisco and works in Mountain View. In the morning, he has 333 transportation options (bus, cab, or train) to work, and in the evening he has the same 333 choices for his trip home. If James randomly chooses his ride in the morning and in the evening, what is the probability that he'll take the same mode of transportation twice?

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Brooklyn · Answer 1

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.