Why E[chosen by both A and B] = 10 * P(chosen by both A and B) directly?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
Related questions
Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55ef11ec-a56d-4e20-a638-de429c981cb2%2Fa125b87c-deff-4e48-8eeb-0a8a62974bff%2Fouo8y13_processed.jpeg&w=3840&q=75)
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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