Question

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. Consider the experiment of picking a random ball from the urn and observing the number printed on the ball. If X is the number observed, what is E[X]?

Answer 1

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,

$P(A)=\dfrac{10}{20}=0.5\\\\ P(B)=\dfrac{6}{20}=0.3\\\\ P(C)=\dfrac{4}{20}=0.2$

If X is the number observed.

Since $E[X]=\sum_{i=1}^{n}x_ip_i$

Then,

$E[X]=5\times P(A)+4\times P(B)+2\times P(C)\\\\=5\times 0.5+4\times 0.3+2\times 0.2\\=4.1$

Hence, E[X]=4.1