Two cards are drawn at random from this deck. Suppose the order matters, so the draws are 2-permutations and not subsets (use permutations and not combinations). i) What is the probability that the second card is blue? # Hint: your denominator is the number of 2-permutations of 45 cards. For the numerator, pick the blue card first, then pick the other card. j) What is the probability that the second card is blue given that the first card is red? ⠀ Hint: try restricted sample spaces. Your denominator is the number of ordered pairs where the first card is red. For the numerator, use two stages: pick the red card first, then pick the blue card. k) What is the probability that the second card is blue given that the first card is blue? Hint: try restricted sample spaces. Your denominator is the number of ordered pairs where the first card is blue. For the numerator, since you are picking two blue cards, you have to use a permutation. I) What is the probability that the second card is blue given that the first card has rank 1? + H Hint: try cases based on the color of the first card. In both cases, work with restricted sample spaces where your denominator is the number of ordered pairs wher the first card has rank 1. Case 1 - the first card is blue: your numerator is the number of ordered pairs where the first card is blue and has rank 1, and the second card is one of the remaining blue cards. Case 2 - the first card is red: your numerator is the number of ordered pairs where the first card is red and has rank 1, and the second card is one of the blue cards.
Two cards are drawn at random from this deck. Suppose the order matters, so the draws are 2-permutations and not subsets (use permutations and not combinations). i) What is the probability that the second card is blue? # Hint: your denominator is the number of 2-permutations of 45 cards. For the numerator, pick the blue card first, then pick the other card. j) What is the probability that the second card is blue given that the first card is red? ⠀ Hint: try restricted sample spaces. Your denominator is the number of ordered pairs where the first card is red. For the numerator, use two stages: pick the red card first, then pick the blue card. k) What is the probability that the second card is blue given that the first card is blue? Hint: try restricted sample spaces. Your denominator is the number of ordered pairs where the first card is blue. For the numerator, since you are picking two blue cards, you have to use a permutation. I) What is the probability that the second card is blue given that the first card has rank 1? + H Hint: try cases based on the color of the first card. In both cases, work with restricted sample spaces where your denominator is the number of ordered pairs wher the first card has rank 1. Case 1 - the first card is blue: your numerator is the number of ordered pairs where the first card is blue and has rank 1, and the second card is one of the remaining blue cards. Case 2 - the first card is red: your numerator is the number of ordered pairs where the first card is red and has rank 1, and the second card is one of the blue cards.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Two cards are drawn at random from this deck. Suppose the order matters, so the draws are 2-permutations and not
subsets (use permutations and not combinations).
i) What is the probability that the second card is blue?
Hint: your denominator is the number of 2-permutations of 45 cards. For the numerator, pick the blue card first, then
pick the other card.
j) What is the probability that the second card is blue given that the first card is red?
●‒‒
Hint: try restricted sample spaces. Your denominator is the number of ordered pairs where the first card is red. For the
numerator, use two stages: pick the red card first, then pick the blue card.
k) What is the probability that the second card is blue given that the first card is blue?
T
Hint: try restricted sample spaces. Your denominator is the number of ordered pairs where the first card is blue. For
the numerator, since you are picking two blue cards, you have to use a permutation.
1) What is the probability that the second card is blue given that the first card has rank 1?
Hint: try cases based on the color of the first card. In both cases, work with restricted sample spaces where your
denominator is the number of ordered pairs wher the first card has rank 1.
Case 1 - the first card is blue: your numerator is the number of ordered pairs where the first card is blue and has rank
1, and the second card is one of the remaining blue cards.
Case 2 - the first card is red: your numerator is the number of ordered pairs where the first card is red and has rank 1,
and the second card is one of the blue cards.
Transcribed Image Text:A deck consists of 45 cards with 5 suits labelled A to E and numbered ranks from 1 to 9. Each card is equally likely
to be drawn.
Suits A to C are red.
Suits D to E are blue.
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