Answer: 4.1
Step-by-step explanation:
Given : An urn contains 10 balls with the number ‘5’ printed on them, 6 balls with ‘4’ printed on them, and 4 balls with ‘2’ printed on them.
Total balls = 10+6+4=20
Let A , B and C are the events of drawing ball with the number ‘5’, ball with the number ‘4’ and ball with the number ‘2’ respectively.
Then,
[tex]P(A)=\dfrac{10}{20}=0.5\\\\ P(B)=\dfrac{6}{20}=0.3\\\\ P(C)=\dfrac{4}{20}=0.2[/tex]
If X is the number observed.
Since [tex]E[X]=\sum_{i=1}^{n}x_ip_i[/tex]
Then,
[tex]E[X]=5\times P(A)+4\times P(B)+2\times P(C)\\\\=5\times 0.5+4\times 0.3+2\times 0.2\\=4.1[/tex]
Hence, E[X]=4.1
