Question

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?

Answer 1

Total number of way to pick 3 letters is 6C3 = 20.

Explanation:

P(E) = 3/6 = 1/2

P(O) = 3/6 = 1/2

The intersection is P(E n O) = P(E)P(O | E)

= 1/2(2/5)

= 1/5

P( E or O but not both) = P(E and not O) + P(O and not E)

(THis step is easier to understand if you shade in a venn diagram for this):

= [ P(E) - P(E n O) ] + [ P(O) - P(O n E) ]

= 1/2 - 1/5 + 1/2 - 1/5

= 1 - 2/5

= 3/5

The P (E or O or both ) is just the union of the two:

P( E U O) = P(E) + P(O) - P(E n O)

= 1/2 + 1/2 - 1/5

= 4/5