Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 4 - Probability and Counting Rules - 4-5 Probability and Counting Rules - Exercises 4-5 - Page 245: 10


a. $0.002$ b. $0.246$ c. $0.751$ d. $0.249$

Work Step by Step

Total red face cards=2*3=6 Total black cards numbered 2–9 = 8*2=16 Total outcomes of draw 4 cards from 22: $_{22}C_4$=7315 a. All 4 cards are red. Choose all 4 from 6 red: $_6C_4$=15, $p=15/7315=0.002$ b. 2 cards are red and 2 cards are black. Choices 2 red from 6 and 2 black from 16: $_6C_2$*$_{16}C_2$=1800, $p=1800/7315=0.246$ c. At least 1 of the cards is red. For no card is red (all black): $_16C_4$=1820, $p=1-1820/7315=0.751$ d. All 4 cards are black. $p=1820/7315=0.249$
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