PROBLEM 10E

A single card is drawn at random from each of six well-shuffled decks of playing cards. Let A be the event that all six cards drawn are different.

(a) Find P(A).

(b) Find the probability that at least two of the drawn cards match.

Answer :

Step 1 of 2:

A single card is drawn at random from each of six well-shuffled decks of playing cards.

Let A be the event that all six cards drawn are different.

a).

Here the first deck will always be a “different” card,so it has probability of is 1.

The second deck has a probability of of being a different card.

The third deck has a probability of ,...,the six deck has a probability of .

Now we have to find the probability of A.

We know that A is the event that all six cards drawn are different.

P(all six cards drawn are different ) = P(A)

P(all six cards drawn are different ) =

P(all six cards drawn are different ) =

P(all six cards drawn are different ) = 0.74141

Therefore the probability of A is 0.74141