# "Compute the probability of #x# successes in the #n# independent trials of the experiment" ?

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I just need someone to show me how the by-hand work goes. I can do this via TI-84 since our professor teaches us to use that.

*Given parameters:*

part (A)

#n=7#
#p=0.5#
#x\gt3#

**Answer:** 0.5

part (B)

#n=12#
#p=0.35#
#x\le4#

**Answer:** #\approx0.5833#

I just need someone to show me how the by-hand work goes. I can do this via TI-84 since our professor teaches us to use that.

*Given parameters:*

part (A)

#n=7# #p=0.5# #x\gt3#

**Answer:** 0.5

part (B)

#n=12# #p=0.35# #x\le4#

**Answer:**

##### 1 Answer

The formula is

and

#### Explanation:

this is a closed form solution but basically what your doing is checking all combinations meaning that for 0 success out of 12 you have only 1 way to accomplish this and that's if they all are failures. 1 success out of 12 you have 12 ways to accomplish this. Each one be success and the rest be failures.... and so on...

but remember that we have the probability of the path to consider and the rule of probabilities for each trial gives us

so in the case of 1 we know

this generalization is only for the probability of exactly 1 success. The question is asking for additional scenarios that x can be so we just sum across those scenarios. These too follow probability rules such that p1 or p2 =

Thus the binomial distribution is a pattern for following the rules of probability when we know that things are mutually exclusive or independent of each other.