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Probability

probability that both cards have rank no higher than 10, and at least one of the cards is red?

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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Question

This problem will refer to a standard deck of cards. Each card in such a deck has
a rank and a suit. The 13 ranks, ordered from lowest to highest, are 2, 3, 4, 5, 6, 7, 8, 9, 10,
jack, queen, king, and ace. The 4 suits are clubs (♣), diamonds (♢), hearts (♡), and spades (♠).
Cards with clubs or spades are black, while cards with diamonds or hearts are red. The deck
has exactly one card for each rank–suit pair: 4 of diamonds, queen of spades, etc., for a total of
13 · 4 = 52 cards. Take a look at the screenshot please!

Suppose you select a card uniformly at random from a standard deck, and then without putting
it back, you select a second card uniformly at random from the remaining cards. What is the
probability that both cards have rank no higher than 10, and at least one of the cards is red?

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