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A card game is played with a deck of 18 cards which can be one of 2 suits, one of the suits being hearts, and one of 9 ranks. A hand is a subset of 3 cards. What is the probability that a hand has exactly two hearts? What is the probability that a hand has exactly two hearts given that it has at least one heart? Hint: use the formula for conditional probability. The denominator, the probability that the hand has at least one heart, can be computed using complements. The numerator is the probability that the hand has exactly two hearts and it has at least one heart, so it has exactly ??? hearts. What is the probability that a hand has exactly two hearts given that it has the 2 of hearts? Hint: try restricted sample spaces.

A card game is played with a deck of 18 cards which can be one of 2 suits, one of the suits being hearts, and one of 9 ranks. A hand is a subset of 3 cards. What is the probability that a hand has exactly two hearts? What is the probability that a hand has exactly two hearts given that it has at least one heart? Hint: use the formula for conditional probability. The denominator, the probability that the hand has at least one heart, can be computed using complements. The numerator is the probability that the hand has exactly two hearts and it has at least one heart, so it has exactly ??? hearts. What is the probability that a hand has exactly two hearts given that it has the 2 of hearts? Hint: try restricted sample spaces.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A card game is played with a deck of 18 cards which can be one of 2 suits, one of the suits being hearts, and one of 9 ranks. A hand is a subset of 3 cards. What is the probability that a hand has exactly two hearts? What is the probability that a hand has exactly two hearts given that it has at least one heart? Hint: use the formula for conditional probability. The denominator, the probability that the hand has at least one heart, can be computed using complements. The numerator is the probability that the hand has exactly two hearts and it has at least one heart, so it has exactly ??? hearts. What is the probability that a hand has exactly two hearts given that it has the of hearts? Hint: try restricted sample spaces. For the denominator, use two stages: count hands that have one specific card, the 2 of hearts, and a subset of any two cards from the rest of the deck. The numerator is the number of hands that have exactly two hearts, with one of them being the 2 of hearts. Try three stages: pick the 2 of hearts, then pick another heart, then pick a third card that is not a heart.
Transcribed Image Text:A card game is played with a deck of 18 cards which can be one of 2 suits, one of the suits being hearts, and one of 9 ranks. A hand is a subset of 3 cards. What is the probability that a hand has exactly two hearts? What is the probability that a hand has exactly two hearts given that it has at least one heart? Hint: use the formula for conditional probability. The denominator, the probability that the hand has at least one heart, can be computed using complements. The numerator is the probability that the hand has exactly two hearts and it has at least one heart, so it has exactly ??? hearts. What is the probability that a hand has exactly two hearts given that it has the of hearts? Hint: try restricted sample spaces. For the denominator, use two stages: count hands that have one specific card, the 2 of hearts, and a subset of any two cards from the rest of the deck. The numerator is the number of hands that have exactly two hearts, with one of them being the 2 of hearts. Try three stages: pick the 2 of hearts, then pick another heart, then pick a third card that is not a heart.
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