Can you suggest how to solve a similar problem on the basis of discrete mathematics and logic?

Question

Discrete Math

The numbers A, B and C independently of each other take two values: 0 and 1,
and they take the value 1 with probability p, q and r, respectively.

What is the probability that the expression
(A||B)&&(A||C) is equal to 1?

Choose one correct answer:
(p+q)(p+r)
p+pq+pr+qr
p+(1-p)qr
p+qr

*I understand how to transform the expression (A||(B&&C) and make a truth table , but I don't understand how to sum the probability.

Answer 1

A||(B&&C) is 1 if A = 1 or B&&C = 1
P(A = 1) = p
P(B&&C = 1) = qr
P(A||(B&&C) = 1) = p + qr - pqr =p+(1-p)qr