This is a sample blog post from the Primary School. ISOCS families have access to live weekly posts describing the learning experiences in their children’s classes.

**The Monty Hall Problem**

Today we furthered our interest and understanding of probability by exploring the The Monty Hall Problem, a seemingly simple game which confounded even mathematicians, as the statistical probability is counter-intuitive.

Problem:

A TV host shows you three numbered doors (all three equally likely),

one hiding a car and the other two hiding goats. You get to pick a

door, winning whatever is behind it. Regardless of the door you

choose, the host, who knows where the car is, then opens one of the

other two doors to reveal a goat, and invites you to switch your

choice if you so wish. Does switching increases your chances of

winning the car?

If the host always opens one of the two other doors, you should

switch. Notice that 1/3 of the time you choose the right door (i.e.

the one with the car) and switching is wrong, while 2/3 of the time

you choose the wrong door and switching gets you the car.

Thus the expected return of switching is 2/3 which improves over your

original expected gain of 1/3 .

Even if the hosts switches only part of the time, it pays to switch.

Only in the case where we assume a malicious host (i.e. a host who

entices you to switch based in the knowledge that you have the right

door) would it pay not to switch.

References

L. Gillman The Car and the Goats American Mathematical Monthly,

January 1992, pp. 3-7. From this website

Still confused? We’re not surprised! The students asked me to share this great video to help explain it!

**Calculating the statistical probability of getting a 7 when you roll two dice**

Once our brains were “warmed up” (!!) I challenged the students to discover which number was most likely to come up if I rolled two 6 faced dice, why that was… and finally calculate the statistical probability of each sum being rolled.

It took a while, but collectively we managed to figure out all 36 possible permutations and relative likelihood of each sum being rolled. We concluded that 7 had the greatest probability because there were 6 out of 36 chances that two numbers totalling seven might be rolled, thus giving it a one in six chance.

In concluding our lessons on probability, I cheekily pointed out that there had been a 90% chance of rain and a 100% chance that we would walk to Teuflibach today, so the students who had brought wet weather clothing were most successfully applying probability in real life!!