this probability situation – If a couple of people decide to travel on separate airliners instead of traveling together, have they halved their chances of dying in a plane crash, or doubled them?
In: 3
You need to define the cases much more clearly.
If you’re talking about the chances either or both of them die, then you’ve increased the chances, as either plane (or both planes) having an issue would fulfill that criteria.
If you’re talking about the chances that both of them die, then you’ve reduced the chances (not halved), because both planes must go down.
If you talking about the chances that exactly one of them dies but the other survives, then you increased the chances, since this was impossible when they were on the same plane. This requires one plane to go down and the other to be fine.
Same average number of deaths but spread over cases where one lives and one dies. For example if the chance of dying was 1/10:
Both people on the same flight
10/100 chance they both die.
Total: 20 deaths per 100 flights.
Different flights
9/100 chance just A dies
9/100 chance just B dies
1/100 chance they both die.
Total: 20 deaths per 100 flights.
As is always the case with statistics, It depends on what you are specifically asking. The chance that any of them individually dies stays the same. The chance that both of them dies decreases as now two planes have to crash to satisfy this condition. The chance that either of them dies increases as you are increasing the amount opportunities for a plane crash to occur.
Planes don’t crash due to “chance”. It’s not as if the plane says “Well I’ve flown 100 times now, on the next flight I feel like crashing”.
That’s why probabilities are a bit of nonsense and don’t really mean anything in the real-world. Planes crash due to causal events like accidents or mechanical failures.
**the chance of both dying is lower if they take the same plane.** Here is the math. Assume each plane has a 25% chance of crashing (so chance of alive is 75%)
**outcomes**: assuming the two planes have [no influence on each other](https://www.mathsisfun.com/data/probability-events-independent.html). We have two people, Abe and Bob. Keeping the probabilities simple.
* **Abe & Bob in same plane** = 25% for both since the chance is the same in either plane.
* **Abe in plane 1 & bob in plane 2**: we now have two events, one for each plane.
* Abe dead bob alive: 0.25 x 0.75 = 18.75%
* Abe alive bob dead: 0.75 x 0.25 = 18.75%
* Abe alive bob alive: 0.75 x 0.75 = 56.25%
* **Abe dea bob dead (your question)**: 0.25 x 0.25 = 6.25%.
I used 25% so you can do it in your head. The same applies to the [tiny probabilities](https://flyfright.com/statistics/) in reality too, just the math is messier.
Let’s ignore the airliner crashes and simplify by going to coins (1 in 2).
If two people use the same coin, they both have a 1/2 chance of H. If they use two coins, 1/4 both H, 1/4 both T, and 1/2 one H, one T.
Each person still have the same probability of H in all cases. The probability of *both* getting H is smaller.
Your question isn’t clear so there’s not really a good way to answer.
Try these: https://www.mathsisfun.com/data/probability-events-conditional.html https://youtu.be/ibINrxJLvlM
The doubled the chances that someone would be involved in a plane crash, but they squared the chance that they will both be in a plane crash.
Let’s say the chance of a plane crashing is 1/100 (not a real number). There are two planes, and each one has a chance of 1/100. The chance that either one goes down is 2/100 or 1/50. The chance that both planes will crash is (1/100)^2 or 1/10000
Traveling together or separate will not change the statistical probability of dying in an aircraft crash. Each individual has the same probability, though depending on which country, airline, airport one will fly with or onto will change the probability.
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