probability question

Question

A box contains letter A,B,C,D,E. Here are the probabilities of randomly picking certain letters from the box: p(A)=1/8, p(B)=1/7, p(C)=1/9, p(D)=1/6, p(E)=unknown. What is the probability of picking an E?

Answer 1

P(E)=1-(P(A)+P(B)+P(C)+P(D))

P(A)+P(B)+P(C)+P(D)=1/8+1/6+1/9+1/7=7/24+16/63=275/504

P(E)=1 - 275/504=229/504