Part b, what is the probability that a randomly chosen red shirt will be small?

Thanks for the full problem. You did part A correctly but wrote "large shirt" instead of "red shirt" in the denominator. You correctly used 0.35, the probability of a red shirt.

The formula for conditional probability applied here says:

P( large | red ) = P(large & red) / P(red)

We have n=100 shirts, 5 of which are large and red

P(large & red) = 5/100

P(red) = 35/100

P(large | red) = (5/100)/(35/100) = 5/35 = 1/7 = 0.14285...

Part A 14.3%

P(small | red) = P(small & red) / P(red) = (30/100)/(35/100)=6/7=.8571...

Part B 85.7%