Given an uniformly-distributed random variable that takes integer values between a and b inclusive.

P(3<=X<=7) = 1/21

P(0<=X<=5) = 1/35

What is P(90<=X<=110) if a<=3 and b>=10?

Shouldn’t the answer be 6/35?

→ Since the distribution is uniform, and 5 integers (3 to 7) contribute 1/21, each integer should contribute 1/105. Also since 3 integers would then contribute 1/35, P(X<=2) = 0. Similar since X takes values between a and b inclusive b should be 107 (to cover total 105 integers)

So P(90<=X<=105) should be P(X=90) + P(X=91) + … +P(X=107) = 18 / 105 = 6/35?