Why Probability is Interesting
What is Probability?
Probability is a measure which tells about the likelihood of occurrence of an event. In a real-world scenario where we can’t say anything with certainty, we use probability to tell how likely something is to happen.
The most simple example of Probability is tossing a coin where the probability of getting head(H) or tail(T) is equally likely which equals to 1/2.
The most basic definition of probability is given by:
P(A) = Number of favourable outcomes / Number of total outcomes
where A is the event/experiment.
I will be talking mostly about some of the most interesting results of probability, skipping the basic definitions in the context of probability theory.
How gambling games company make money and offer you free drinks
Let’s suppose you play a bet for $10 and the winning amount is $100 if you win the bet. The game is simple, you have to make a three-digit number out of 000–999 and a lucky draw will declare a winning number out of 000–999. If your number matches, you’ll take $100 otherwise you’ll pay $10.
It sounds like a good deal. Play the bet and if win, take $100.
But wait, let’s do the mathematics here. Probability plays a significant role here.
P(getting winning number) [P1] = 1/1000 = 0.001
Amount won, if you win the bet [X1] = $100
P(not getting winning number) [P2] = 1–1/1000 = 999/1000 = 0.999
Amount lost, if you lose the bet [X2] = -$10
We have written the loss with a negative sign to calculate the expected amount you’ll receive on playing one bet.
Expected Value
The expected value (EV) is a weighted average of all possible outcomes, whereas the weights are represented by probabilities. The expected value is the mean value.
In general, EV is calculated as:
EV = x1p1 + x2p2 + … + xnpn
where EV is the expected value, x1 … xn are possible outcomes and p1… pn are respective probabilities of the outcomes to happen.
EV on playing one bet = P1X1+P2X2
= 0.001*100 + 0.999*(-10)
= 0.1–9.99
= -9.89
The EV comes out to be negative, meaning the player’s disadvantage and equivalently, house advantage. In simple words, after every bet, the house will be making a profit of $9.89. This is the profit of one bet only.
Let’s suppose there are 100 games per day. Then, the house makes a profit of 9.89*100 = $989.
In one month, it makes a profit of $989*30 = $29,760
In one year, it makes a profit of $989*365 = $360,985
which is a large amount.
Now, if a company is making a profit of $989 per day. They can surely offer free drinks to their players to keep them engaged in games and let them play more games there. Interesting? Quite interesting.
Birthday paradox
Birthday paradox states that in a room having n people, some pairs will share their birthdays. The interesting part about it is that if n = 23, meaning the room contains 23 people, the probability is 50% that at least two individuals will share their birthdays. It boosts the interest more when n increases to 60, there is a 99.4% chance that at least two individuals will share their birthdays.
You can find the mathematics here.
Finding the value of PI without circle or diameter
We all know PI. One of the most interesting irrational and transcendental number. The most common definition of PI we have studied is that it is the ratio of the circumference of a circle with its diameter.
Interestingly, we can estimate the value of PI in another way as well. It is quite interesting that the value of PI is directly related to the probability of a very famous and common experiment that is the dropping needle experiment.
Let suppose we have a needle of length d. We draw some parallel lines d distance apart and start dropping the needle. The probability of needle crossing the lines comes out to be 2/PI.
#needles crossing the line / #needles tossed = 2/PI
Rearranging the equation,
PI = 2 * #needles tossed / #needles crossing the line
The value will be more approximate to PI if we increase n, where n is #needles tossed.
Experimental results show that value comes out to 3.14159… for n=100,000. Interesting, right?
These are very limited instances where probability rules the world. There can be many more and probability is your friend, don’t run from it. It will help you always. 🤓
Some Interesting Facts about Probability
Odds of being a victim of a serious crime — 1 in 20
Odds of being arrested while drunk driving — 1 in 200
Odds of being born with 11 fingers or toes — 1 in 500
Odds of dying from an injury in the next year — 1 in 1,820
Odds of dying in a car accident — Between 1 in 4,000 and 1 in 8,000
Odds of winning an Oscar (given you’re in Industry) — 1 in 11,500
Odds of finding a pearl in an oyster — 1 in 12,000
Odds of becoming a professional athlete — 1 in 22,000
Odds of going blind after laser eye surgery — 1 in 85,714
Odds of dating a supermodel — 1 in 88,000
Odds of dying in an aeroplane crash — 1 in 354,319
Odds of getting killed by fireworks — 1 in 616,488
Odds of becoming a billionaire — 1 in 7,000,000
Odds of becoming President of the U.S. — 1 in 10,000,000
Odds of getting attacked by a shark — 1 in 11,500,000
Odds of winning $1,000 in the McDonald’s Monopoly game — 1 in 36,950,005
Odds of winning the Mega Millions lottery — 1 in 135,145,920
At least you can still be president, right? 🥳
I’m a newbie in writing articles. Do let me know about suggestions and corrections, if any. Thanks for reading! 🤓
