Question

In the carnival game "chuck-a-luck", you pick a number from 1 to 6 and roll 3 dice in succession. If your number comes up all three times, you win $3; if your number comes up twice, you win $2; if it comes up once, you win $1; otherwise you lose $1. What is your expected value

Answer 1

Answer:

42 cents

Step-by-step explanation:

Data provided in the question:

Random variable i.e gain  with values 3,2,1,-1.

Now,

The corresponding probabilities will be as follows:

$P(3)=(\frac 16)^{3}$

$P(2)=3\times(\frac 16)^{3}$

$P(1)=3\times(\frac 16)^{3}$

$P(-1)=1-7(\frac 13)^{3}$

Expected gain = $3\times(\frac 16)^{3}+2\times3\times(\frac 16)^{3}+1\times3\times(\frac 16)^{3}-1\times\left(1-7\times(\frac 13)^{3}\right)$

Expected gain = $(\frac 13)^{3}[3+6+3-(0.7407)]$

$=(\frac 16)^{3}[11.2593]=0.4170$

≈ 42 cents