I know the independent concept and multiplication rules.Example Flip Coin5 times flip, how many times success of Head?Ans : 1 2 ⋅ 1 2 ⋅ 1 2 ⋅ 1 2 ⋅ 1 2 = 1 32 Why do we use multiplication rules, not other rules?I know if we use addition then probability 2.5 which is invalid because probability should be between 0 to 1. Same for Subtraction and division.But, I am still confused why we use multiplication? What is the basic and core logic behind this?Can anyone tell me the concept of this?

Question

I know the independent concept and multiplication rules.Example Flip Coin5 times flip, how many times success of Head?Ans :       1    2    ⋅      1    2    ⋅      1    2    ⋅      1    2    ⋅      1    2    =      1    32  Why do we use multiplication rules, not other rules?I know if we use addition then probability 2.5 which is invalid because probability should be between 0 to 1. Same for Subtraction and division.But, I am still confused why we use multiplication? What is the basic and core logic behind this?Can anyone tell me the concept of this?

trantegisis · Accepted Answer

Given two events   A and   B, then the conditional probability of   A given   B (the probability of   A if we know that   B has occured) is defined as  P  (  A      |    B  )  =            P      (      A      ∩      B      )              P      (      B      )        ,for this conditional probability, when the occurrence of   A is independent of   B, then we have  P  (  A      |    B  )  =  P  (  A  )  ,it is clear from the two equations above two events   A and   B are defined to be statistically independent if    ⟹    P  (  A  ∩  B  )  =  P  (  A  )  P  (  B  )  .which means the information about the value of one event provides no information about the happening of the other event.Now, suppose we consider the toss of 5 coins at the same time, the probability of occurrence of 5 heads   h  h  h  h  h is:  P  (  h  h  h  h  h  )  =      1    2    ×      1    2    ×      1    2    ×      1    2    ×      1    2    .here, you can consider that there are   2  ×  2  ×  2  ×  2  ×  2 occurrences from which one is the case that we desired:   h  h  h  h  h  h, hence the probability for this case is:       1          2      5      .

Jamison Rios · Accepted Answer

Lets first simplify the problem to 1 flip and work from there. If we have one flip, we&#039;ve got 2 options: h (heads) or t (tails).If we throw 2 coins, we&#039;ve got 4 options: ht,th,hh,tt all of which have an equal chance of happening.Move to 3 coins and we get 8 options: hhh,hht,hth,thh,htt,tht,tth,ttt. Again, all of which have an equal chance of happening. It will be obvious that the different possibilities keep doubling because every throw has 2 options. If instead we roll a 6 sided die, we&#039;d have to multiply the total amount of options by 6.This being said, we still divide our &quot;positive&quot; result by all the options. So in your example the only positive result is hhhhh which means that there&#039;s 1 positive result in a total of 32 options. (You can look at it as an out branching tree.) Therefore the chance is       1    32  .

I know the independent concept and multiplication rules. Example Flip Coin 5 times flip, h

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