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Why E[chosen by both A and B] = 10 * P(chosen by both A and B) directly?

Why E[chosen by both A and B] = 10 * P(chosen by both A and B) directly?

A First Course in Probability (10th Edition)
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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Why E[chosen by both A and B] = 10 * P(chosen by both A and B) directly?

7.7 Suppose that A and B each randomly and independently choose 3 of 10 objects. Find the expected number of objects a. chosen by both A and B; b. not chosen by either A or B; c. chosen by exactly one of A and B. a. P(A) = P(B) = 1/3/2 Since A and Bare independent, Pichosen by both A and B) = P(ANB)=P(A) P(B) = 100 9 ។ 9 ECANB] = 10 x 101 102 = 11/1/20 b⋅ P(A²)=P[B²) = √2/² Plnot chosen by either for B) = P(A²1B³²) = 42 E [A²MB] = 10x 69 = 49 lox 100 c. P[chosen by Ano+B) = 1/23/² P[chosen by B not A = 21 X း 49 100 시의 7/8 42 E [ chosen by exactly one of AandB) - Yox 2x = = = = = (၁၁ 10 2 44 P
Transcribed Image Text:7.7 Suppose that A and B each randomly and independently choose 3 of 10 objects. Find the expected number of objects a. chosen by both A and B; b. not chosen by either A or B; c. chosen by exactly one of A and B. a. P(A) = P(B) = 1/3/2 Since A and Bare independent, Pichosen by both A and B) = P(ANB)=P(A) P(B) = 100 9 ។ 9 ECANB] = 10 x 101 102 = 11/1/20 b⋅ P(A²)=P[B²) = √2/² Plnot chosen by either for B) = P(A²1B³²) = 42 E [A²MB] = 10x 69 = 49 lox 100 c. P[chosen by Ano+B) = 1/23/² P[chosen by B not A = 21 X း 49 100 시의 7/8 42 E [ chosen by exactly one of AandB) - Yox 2x = = = = = (၁၁ 10 2 44 P
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