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I am really struggling with statistics. I am trying to come up with the basic equation/concept of calculating the probability for something.

for example: I know that the probability of coming up with exactly 3 heads in 4 flips of a coin is 1/4, but I don't know why (other than writing out all possibilities- but I can't apply that to large numbers).

heres what I know so far: Each flip has a 1/2 Chance of coming up heads, meaning you have two possibilities with each flip. I know then that the number of total possible outcomes for this particular example is 2^4 (possibilities ^ # of tries). I just don't know how to apply that so I can come up with the general equation for the probability of something.

another example: rolling a die 2x and having it come up with even numbers both times.

Lydia
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1 Answers1

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If events are independent, then you can calculate the probability of sequential events by multiplying the probability of each event.

e.g. $p_1 \times p_2$ for two coin flips, where each $p_i=1/2$

Every time an event is generated in a sequence, multiply the probability of that event. That will give you the probability of that sequence. The probability of all possible sequences should add up to one.

When flipping a coin or rolling a die, the coin or die has no idea what the previous flip or roll was, so those events are "independent."

Sometimes outcomes are similar. For example, the statement "3 heads in four tosses" can be any one of {H,H,H,T}, {H,H,T,H}, {H,T,H,H}, {T,H,H,H}. When order is not important it is called a combination. In that case you want to multiply the probability of the sequence times the number of ways it can occur to create the same combination, ie "3 heads in four tosses".

The binomial theorem is helpful when dealing with combinations of independent events.

mandata
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  • Maybe i'm misunderstanding you, but I don't get the correct answer if I do that? 1/21/21/2*1/2 = 1/16, not 1/4 which is what the answer is.... – Lydia May 05 '15 at 02:49
  • Sorry, I should edit my response, let me do that. – mandata May 05 '15 at 02:52
  • so theres no real general solution? i would just have to write it out??? – Lydia May 05 '15 at 03:02
  • There are formulas (like the binomial theorem). Once you have the concepts down, they will be easy to learn. When the problem is small, it is often easy just to write it out. – mandata May 05 '15 at 03:05