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Compute the probability that a hand of 13 cards
Chapter 2, Problem 55P(choose chapter or problem)
Problem 55P
Compute the probability that a hand of 13 cards contains
(a) the ace and king of at least one suit;
(b) all 4 of at least 1 of the 13 denominations.
Questions & Answers
QUESTION:
Problem 55P
Compute the probability that a hand of 13 cards contains
(a) the ace and king of at least one suit;
(b) all 4 of at least 1 of the 13 denominations.
ANSWER:
Solution:
Step 1 of 2:
We know that in a hand we will be having 13 cards.
- The claim is to find the probability that the ace and king of at least one suit.
Let = event that the hand has an ace and a king in the suit i for i = 1, 2, 3, 4.
We want P()
Then P() =
-
+
-
=
=0.058823.
) =
= 0.002641
) =
= 8.4289
=
= 1.710
Then, P() =
(0.058823) -
(0.002641) +
(8.4289
) -
(1.710
)
= 0.0808.
Hence, the probability that the ace and king of at least one suit is 0.0808.