# Tutoring probability, you can imagine so many everyday examples. The tutor shares one.

This morning I went to pick up some groceries.

I like to load groceries through the rear door of the van. However, I also like to drive forward from a parking space, rather than backing up.

I arrived at the supermarket early, so there were many free parking spaces two deep: you could park in the first one or glide through to the second one, which faces an exit lane.

So here are the risks of the game:

1. Park in the first row, forwards: you have definite access to your rear hatch but you will have to back out if someone parks in front of you.
2. Park in the second row, forwards: you can definitely drive out forwards, but someone may park behind you, blocking your rear hatch.
3. Park too close and the relevant possibility above (1 or 2) is much more likely; park further away and it takes longer to walk in and return (and I was, as always, in a hurry).

I opted for a fairly close spot and parked in the second row for guaranteed forward exit. However, I left two empty slots closer to the store. Would someone park behind me?

When I emerged, no one had parked behind me. However, someone had parked right beside me in the same manner as I, one space nearer the store. Obviously, they are willing to move a little closer to the edge.

Did someone park behind them? Who knows:) It’s interesting that they seem to calculate the situation very similarly to how I do:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring statistics, you might imagine everyday situations. The tutor brings up one.

Let’s imagine we have two mile runners. Runner 1, called R1, has mean time 4:45, with standard deviation 10s; R2 has mean time 5:00 with standard deviation 12s.

In any given race, give the probability R1 will beat R2.

Solution:

First, we convert the mile times to seconds: R1’s mean is 285s, while R2’s is 300.

The expected difference between R2 and R1’s time is 300-285=15.

We can’t add standard deviations, but rather variances: 10^2 + 12^2 = 244. The standard deviation of the difference is then 244^0.5 = 15.6.

The standardized statistic is z = (x-15)/15.6. We wonder p(x>0), which means p(z>-0.96). From the z-table, the answer is 0.8315.

So, R1 should beat R2 about 83% of the time.

Source:

Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics. Don Mills: Addison-Wesley, 1993.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# Tutoring probability, a better example than this might be hard to find. The tutor explains about the Las Vegas square in Careers® by Parker Brothers.

I explain expected value in my post from August 16, 2013, showing by example that the expected value of rolling a fair six-sided die is 3.5.

My younger son and I have played Careers® often at times. From early on, he has enjoyed the Las Vegas square. On that square, the player pays \$3K, then gets back \$1K multiplied by the roll of one die.

With the expected value of the roll being 3.5, the player is expected to receive \$3500, so come out ahead by \$500 each time, on average. I wonder if, intuitively, my son realized that soon after we started playing, when he would have been around 7 years old.

I don’t imagine Las Vegas in real life gives as promising odds as Las Vegas in Careers®.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

# The tutor reports an interesting statistic.

In 2013, the world population was approximately 7.07 billion. At the same time, people aged ≥ 100 numbered about 450 thousand. Those figures suggest that a completely random person on Earth has probability 450 000/7 070 000 000 = 0.000064 of reaching age 100 or greater.

The probability equates to about 64 in one million.

Source:

ieet.org

www.worldometers.info

Oracle Tutoring by Jack and Diane, Campbell River, BC.