Three letters are chosen at random from the word POSTER. What is the probability that the selection will contain E or O but not both? E or O or both?
+23246 There are a total of 6 distinct letters in the word POSTER.
The number of ways to choose three letters from these six letters is: 6C3 = 20.
To choose a set that contains an E or an O but not both, you must choose one of these two letters and the
number of ways to choose one letter from a set of two is: 2C1 = 2.
The other two letters must come from this set of four letters: {P, S, T, R}. The number of ways to choose two
letters from a set of four is: 4C2 = 6.
So, the probability of choosing an E or an O but not both is: 4C2 ·2C1 / 6C3 = 6·2 / 20 = 12/20.
If you are to choose both the E and the O, you must choose two letters from a set of two: 2C2 = 1.
You must now choose one letter from the set of four remaining letters; 4C1 = 4.
So, the probability fo choosing both an E and an O is: 4C1 · 2C2 / 6C3 = 4 · 1 / 20 = 4/20.
To select either one of the two vowels or both of the vowels, add these two answers together:
12/20 + 4/20 = 16/20.
