SOA Exam P Question 172 | Law of total probability for Uniform Distribution

A policyholder has probability 0.7 of having no claims, 0.2 of having exactly one claim,
and 0.1 of having exactly two claims. Claim amounts are uniformly distributed on the
interval [0, 60] and are independent. The insurer covers 100% of each claim.
Calculate the probability that the total benefit paid to the policyholder is 48 or less.
(A) 0.320
(B) 0.400
(C) 0.800
(D) 0.892
(E) 0.924

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[Julia-ywly]

Hi, to be honest I am struggling with how you get the triangle for p(x =2). If anyone could help me it would be greatly appreciated. Thanks! Like how do we find the joint distribution for two claims if one is uniform on 0, 60. We don't add. Is it a double integral? I'm so confused. Thank you!