Joint Probability of Independent Events

In summary, the conversation was about mathematics related to Pokemon, specifically the odds of encountering shiny Pokemon and the probability of them being male or female. The conversation also included a request for someone to double check the calculations and provide explanations if needed. The expert confirmed the accuracy of the calculations and provided additional information and resources for understanding the concept.
  • #1
Subliminal1
16
0
Hello,
I'd like someone to double check my maths please, it wasn't the greatest at school and that was a few years ago!
If I am incorrect could you please tell me the correct answer as well as show me how to apply it so I can figure out similar problems myself. Thanks.

Yes, this is about Pokémon, but there is a lot of maths involved. Here goes:

PROBLEM 1:
For a Pokemon to be "shiny" the odds are 1/273 encounters.
Each encounter has the chance for "Pokemon A" to appear of 60% OR"Pokemon B" to appear of 40%.

The odds of having Pokemon A appear shiny are 1/455
I multiplied 1/273 by 6/10 to result in 1/455.
The odds of having Pokemon B appear shiny are 2/1365
I multiplied 1/273 by 4/10 to result in 2/1365.

PROBLEM 2:
For a Pokemon to be shiny the odds are 1/273 encounters.
5 Pokemon appear in each encounter and always 5, never more, never less. Each has the same odds of being shiny.

The chance that two Pokemon will be shiny in a single encounter are 1/74529
I squared/ multiplied by the power of 2, 273 to result in 1/74529

Applying this maths, the chance of all 5 to be shiny will be 273 to the power of 5?

PROBLEM 3:
I am unsure how to work this one out.
For a Pokemon to be shiny the odds are 1/273 encounters.
Each encounter has the chance for Pokemon A to appear of 60% OR Pokemon B to appear of 40%.
Pokemon A and B both have a 50% chance to be MALE and 50% chance to be FEMALE.

What are the chances of encountering a FEMALE Shiny Pokemon A?

Please let me know if my maths is correct, if it isn't please correct me and show me how to apply it too.

Many thanks!
 
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  • #2
Subliminal said:
Hello,
I'd like someone to double check my maths please, it wasn't the greatest at school and that was a few years ago!
If I am incorrect could you please tell me the correct answer as well as show me how to apply it so I can figure out similar problems myself. Thanks.

Yes, this is about Pokémon, but there is a lot of maths involved. Here goes:

PROBLEM 1:
For a Pokemon to be "shiny" the odds are 1/273 encounters.
Each encounter has the chance for "Pokemon A" to appear of 60% OR"Pokemon B" to appear of 40%.

The odds of having Pokemon A appear shiny are 1/455
I multiplied 1/273 by 6/10 to result in 1/455.
The odds of having Pokemon B appear shiny are 2/1365
I multiplied 1/273 by 4/10 to result in 2/1365.

PROBLEM 2:
For a Pokemon to be shiny the odds are 1/273 encounters.
5 Pokemon appear in each encounter and always 5, never more, never less. Each has the same odds of being shiny.

The chance that two Pokemon will be shiny in a single encounter are 1/74529
I squared/ multiplied by the power of 2, 273 to result in 1/74529

Applying this maths, the chance of all 5 to be shiny will be 273 to the power of 5?

PROBLEM 3:
I am unsure how to work this one out.
For a Pokemon to be shiny the odds are 1/273 encounters.
Each encounter has the chance for Pokemon A to appear of 60% OR Pokemon B to appear of 40%.
Pokemon A and B both have a 50% chance to be MALE and 50% chance to be FEMALE.

What are the chances of encountering a FEMALE Shiny Pokemon A?

Please let me know if my maths is correct, if it isn't please correct me and show me how to apply it too.

Many thanks!

Hi Subliminal,

Considering each Pokemon is created independently from others your math is correct. For more information on why this works refer >>this<<. For the last question, the probability that the Pokemon is female is $\frac{1}{2}$, the probability that A appears is $\frac{60}{100}$ and the probability that it is shiny is, $\frac{1}{273}$. Considering these three events as independent the joint probability is, $\frac{1}{2}\times\frac{60}{100}\times\frac{1}{273}$.
 
  • #3
Hi Sudharaka,

I'm glad all those years at school actually got through to me - so "that" is what school is for!

But seriously, thank you for your reply so soon, it was well explained also.

Cheers
John/ Sub
 
  • #4
Subliminal said:
Hi Sudharaka,

I'm glad all those years at school actually got through to me - so "that" is what school is for!

But seriously, thank you for your reply so soon, it was well explained also.

Cheers
John/ Sub

You are very welcome. :)
 

FAQ: Joint Probability of Independent Events

What is the definition of joint probability of independent events?

The joint probability of independent events is the likelihood that two or more events will occur simultaneously, given that they are not influenced by each other. In other words, the probability of one event does not affect the probability of the other event happening.

How is joint probability calculated?

The joint probability of independent events is calculated by multiplying the individual probabilities of each event. For example, if the probability of event A is 0.5 and the probability of event B is 0.3, then the joint probability of both events occurring is 0.5 x 0.3 = 0.15.

What is the difference between joint probability and conditional probability?

Joint probability is the probability of two or more events occurring simultaneously, while conditional probability is the probability of one event occurring given that another event has already occurred. Joint probability assumes that the events are independent, while conditional probability takes into account the relationship between the events.

How is joint probability used in real-life scenarios?

Joint probability is used in various fields such as economics, medicine, and engineering to calculate the likelihood of multiple events occurring at the same time. For example, in medical research, joint probability is used to determine the effectiveness of a treatment by looking at the probability of both the treatment being successful and the patient's recovery.

What is the importance of understanding joint probability?

Understanding joint probability is crucial in making informed decisions and predictions based on multiple events. It allows us to calculate the likelihood of multiple events occurring simultaneously and helps us make more accurate predictions and assess risks. It is also an essential concept in many statistical and mathematical models used in various industries.

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