Question 1190084
please help me solve this problem about binomial probability
Liz and Robert are competing to see who can ride their bikes around the neighborhood faster. 
Robert wins 55% of the time.If they race ten times, what is the probability that Robert 
will win 7 of the races?
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            This problem is about binomial probability (as you just know).



<pre>
The number of trials is n= 10;  the number of successful trials is k= 7; the probability of success for each single individual trial is p= 0.55.



     A general formula to calculate the probability of k success of n trials is  P(n,k,p) = {{{C[n]^k*p^k*(1-p)^(n-k)}}},
     where {{{C[n]^k}}} = {{{n!/(k!*(n-k)!)}}} are binomial coefficients.



     Substituting given values into the formula, you get

         P(n=10, k=7, p= 0.55) = {{{C[10]^7*0.55^7*(1-0.55)^(10-7)}}} = {{{((10*9*8)/(1*2*3))*0.55^7*0.45^3}}} = 0.1665   (rounded).    <U>ANSWER</U>
</pre>

Solved.


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If you want to see many similar &nbsp;(or different) &nbsp;solved problems, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> 

in this site.


After reading these lessons, &nbsp;you will be able to solve such problems on your own.