Each letter of the alphabet is written on a separate sheet of paper and placed in a box. Find the probability of drawing a vowel, [a,e,i,o,u], or a letter in the word "segments"?
We use the formula
P(A or B) = P(A) + P(B) - P(A and B)
A = drawing a vowel, i.e., one of these five: {a,e,i,o,u}
B = drawing a letter in the word "segments", i.e., one of these six: {s,e,g,m,n,t}
P(A) = 5 out of 26 = 5/26
P(B) = 6 out of 26 = 6/26
P(A and B) = P(drawing an "e") = 1 out of 26 = 1/26
P(A or B) = P(A) + P(B) - P(A and B) = 5/26 + 6/26 - 1/26 = 10/26 = 5/13
Edwin