# Probability with normal distributions

## Homework Statement

The time taken by Smith to travel from A to B is a random variable which follows the normal distribution , with mean 5 minutes and standard deviation 1 minute. The time taken by Jones to travel from A to B follows the normal distribution with mean 15 minutes and SD 2 minutes and is independent of the time taken by Smith. Smith and Jones start to move from A to B at the same time. Smith takes only 4 minutes to reach B and then he returns to A. Determine, up to 3 significant figures the probability that Smith will return to A after Jones arrive at B.

## The Attempt at a Solution

Do i calculate the probability that Jones take less than 4 mins to reach B? If so, the probability is simply 0 so this is wrong.

Or do i take this as a conditional probability question since Jones is known to have arrived at B? If so, i am stucked here.

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Smith's time is 4 + X where X ~ N(5,1).
Jones's time is Y where Y ~ N(15,2).
You want to find P(4 + X > Y).

This is assuming the time it takes to get from B to A has the same distribution as the time to get from A to B.

Smith's time is 4 + X where X ~ N(5,1).
Jones's time is Y where Y ~ N(15,2).
You want to find P(4 + X > Y).

This is assuming the time it takes to get from B to A has the same distribution as the time to get from A to B.
thanks awkward, that seems to be the probability that smith has returned to A once jones reaches B.

i interpreted it as the prob that smith is about to move from B once jones has reached B but this probability is 1 so i will take your suggesttion. thanks!