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A single card is drawn at random from each of six
Chapter 1, Problem 10E(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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:
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