two cards are drawn at random from ten cards numbered 1 to10.Find the expectation of the sum of points on two cards
Answers
Answer:
11
Given :
Two cards are drawn at random from ten cards numbered 1 to 10.
To Find :
the expectation of the sum of points on two cards.
expectation of the sum of points on two cards = 11
Explanation:
Assuming simultaneous draw hence order is immaterial
Total ways to draw 2 cards = ¹⁰C₂ = 45
Sum f cases
x
3 1 1,2
4 1 1,3
5 2 1,4 2,3
6 2 1,5 2,4
7 3 1.6 2,5 3,4
8 3 1,7 2,6 3,5
9 4 1,8 2,7 3,6 4,5
10 4 1,9 2,8 3,7 4,6
11 5 1,10 2,9 3,8 4,7 5,6
12 4 2,10 3,9 4,8 5,7
13 4 3,10 4,9 5,8 6,7
14 3 4,10 5,9 6,8
15 3 5,10 6,9 7,8
16 2 6,10 7,9
17 2 7,10 8,9
18 1 8 , 10
19 1 9,10
P(x) = f/∑f = f/45
expectation of the sum of points on two cards. = ∑xP(x)
= 495/45
= 11