Answer:
The expected number of spots showing on the thrown dice is 30.
Step-by-step explanation:
The expected value of the sum of a random number of independent and identically distributed random variables (which are also independent of the number of random variables as well) equals the expected value of the number of random variables times the expected value of any one of the random variables.
The expected number of dice thrown is
np = 10(0.86) = 8.6
The expected number of spots on any one die is
[tex]\frac{(1+2+3+4+5+6)}{6}[/tex]
=> [tex]\frac{21}{6}[/tex]
=>3.5
So the expected value of the total number of spots on the thrown dice is (10)(0.86)(3.5) =30.1 [tex]\approx[/tex] 30
