The probability that a train arrives late at a particular station is 2

We are given that the probability that a train arrives late is 1/4.

We need to determine the probability that at least 3 trains arrive late. That is, we need to determine the probability that exactly 3 trains arrive late or that all 4 trains arrive late.

Let’s start with 3 late trains and 1 on-time train (L = late and T = on time):

P(L-L-L-T) = 1/4 x 1/4 x 1/4 x 3/4 = 3/256

Since we can organize the 3 Ls and 1 T in 4!/3! = 4 ways, the total probability is actually 3/256 x 4 = 12/256.

Next we can determine the probability that all 4 trains arrive late:

P(L-L-L-L) = 1/4 x 1/4 x 1/4 x 1/4 = 1/256

Thus, the probability of at least 3 trains arriving late is 12/256 + 1/256 = 13/256.

Answer: C

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