Question $2$: It takes a professor a random time between $20$ and $27$ minutes to walk from his home to

school every day. That is$,$ you can assume that the walking time between his home and school is a

uniform random variable.

a$.$ If he has a class at $9$:$00$ A$.$M$.$ and he leaves home at $8$:$37$ A$.$M$.,$ find the probability that he reaches

his class on time.

b$.$ If you know that he leaves home at $8$:$37$ A$.$M and reaches his class that starts at $9$:$00$ A$.$M$,$ what is

the probability that he walks from home to school in is less than $22$ minutes?