Each of the first 6 letters of the alphabet is printed on a separate card. The...

Each of the first 6 letters of the alphabet is printed on a separate card. The letter “a” is printed twice. What is the probability of drawing 4 cards and getting the letters f, a, d, a in that order? Same question if the order does not matter.

Expert Solution

We have total 7 cards: 6 cards for each letter and one more card for letter a.

Out of 7 cards, 1 card is f so probability of letter f card at first draw is 1/7.

After that out of remaining 6 cards, 2 cards are letter a so probability of getting letter a card in second draw is 2/6.

After that out of remaining 5 cards, 1 card is letter d so probability of getting letter d card in third draw is 1/5.

After that out of remaining 4 cards, 1 card is letter a so probability of getting letter a card in fourth draw is 1/4.

Therefore the probability of drawing 4 cards and getting the letters f, a, d, a in that order is

(1/7) * (2/6) * (1/5) * (1/4) = 0.0024

-------------------------

Now order of cards is not important so we can use combination.

Number of ways of selecting 4 cards out of 7 is C(7,4) = 35.

Number of ways of selecting 2 letter a cards, 1 letter f cards and 1 letter d card is

C(2,2) * C(1,1) * C(1,1) = 1

The required probability is

1 / 35 = 0.0286

milcah answered 2 months ago

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