In order to help pay your tuition bills you have decided to go to Las Vegas and

Question

In order to help pay your tuition bills you have decided to go to Las Vegas and try your luck at Blackjack using the following methodology for card counting.

Cards ..Count ...Cards .....Count ...Cards ...Count ...Cards ..Count
Ace..................3.................... 7 ..................Jack
1 ........-2......... 4 ..........-1 ......8........ +1 ......Queen ...+2
2 ....................5 ....................9.................. King
......................6 ....................10

What is the mean and variance of your card counting distribution?

If we make the assumption of normality, what is the probability that your count will be less than -3 or greater than +3?

Explanation / Answer

The mean is -2 + -1 +1 +2 all over 13 so the mean is 0. Variance is 4 + 1 + 1 + 4 = 10. So assuming normality, with a standard deviation of .892. Therefore, 3 away is 3.36 standard deviations away. Looking at a z-table, we have .0008 probability that the count will be less than -3 or greater than +3.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.