Question

Find the variance of the amount of money the contestant wins in given scenario:

On an imaginary television show, there are five identical closed boxes. One box contains $10,000, two boxes contain $1000 each, one box contains $1, and the last box contains a miniature stop sign. A contestant is allowed to select a box, open it, and keep the contents. The contestant is allowed to repeat this process until the box with the stop sign is opened; at this point, the game ends.

Answer 1

Solution:

Let x= number of box

suppose that ,

1 represents a box containing $10000

2 represents a box containing $1000

3  represents a box containing $1

4 represents a box containing stop sign

x	1	2	3	4
P(x)	1/5	2/5	1/5	1/5

= 1(1/5)+2(2/5)+3(1/5)+4(1/5)

= (1/5)+(4/5)+(3/5)+(4/5)

= 12/5

Mean = 2.4 (i.e 2+0.4(3)=1000+0.4(1)=$1000.4)

  

  

V(x) =6.8-(2.4)2=1.04 (i.e 1+0.04(2) = 10000+0.04(1000)= $10040)