Distribution of a random variable

We have two independent random variables: X which has a chi-square distribution and Y which is Bernoulli with parameter p=1/2.

We have then a variable Z = | X-3Y | and we want to compute P(Z<70). Through the disintegration formula we have: P(Z<70) = P(|X-3Y|<70) = P(|X|<70 | Y=0)P(Y=0) + P(|X-3|<70 | Y=1)P(Y=1)

P(|X|<70 | Y=0) = P(X<70 | Y=0) because X is a positive random variable.

P(|X-3|<70 | Y=1) is the problem...my professor, in his solution, wrote that

P(|X-3|<70 | Y=1) = P(X-3<70 | Y=1) = P(X<67 | Y=1)

while I think it should be

P(|X-3|<70 | Y=1) = P(-70< X-3 <70 | Y=1) =

P(-73 < X < 0 | Y=1) + P(0 < X < 67 | Y=1) = 1 + P( X < 70 | Y=1)

which one is the correct answer??