Thread: Choosing letters with replacement.

Five identical cards are labelled A, B, C, D, E. The cards are placed in a box and a card is selected at random. This card is replaced in the box, and a second random selection is made.

a) Draw a grid to show the 25 possible outcomes.
b) Given that neither card has a letter which appears in the word VICTORY, calculate the probability that both are vowels.

I need help with b). What I did was consider it conditional probability. So I found the probability that both are vowels and don't appear in VICTORY which is 4/25 and I divided it by 1 becuase none of them appear in VICTORY. But my answer is wrong.

I looked back at my work from the beginning of the semester and I divided by 16/25 instead, which was correct. But now I can't see why I would divide by 16/25.

Does anyone know?

Originally Posted by bhuang

Five identical cards are labelled A, B, C, D, E. The cards are placed in a box and a card is selected at random. This card is replaced in the box, and a second random selection is made.

a) Draw a grid to show the 25 possible outcomes.
b) Given that neither card has a letter which appears in the word VICTORY, calculate the probability that both are vowels.

I need help with b). What I did was consider it conditional probability. So I found the probability that both are vowels and don't appear in VICTORY which is 4/25 and I divided it by 1 becuase none of them appear in VICTORY. But my answer is wrong.

I looked back at my work from the beginning of the semester and I divided by 16/25 instead, which was correct. But now I can't see why I would divide by 16/25.

Does anyone know?

Hi bhuang,

C is the only letter of the 5 in VICTORY.

Hence, A and E are two vowels of the 4 letters A, B, D, E that do not appear in VICTORY.

Hence the probability that 2 cards do not appear in VICTORY is



then the probability that the two cards are vowels is as you calculated.

Given that the cards do not appear in VICTORY,
there are 16 possibilities in choosing 2 cards.
There are 4 ways to choose the vowels with replacement... AA, AE, EE, EA

therefore there is a 1 in 4 chance the letters were vowels if the letters were not in VICTORY.

Hence, in terms of conditional probability