SOLUTION: 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 ti

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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?
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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). 


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%5Bn%5D%5Ek%2Ap%5Ek%2A%281-p%29%5E%28n-k%29,
     where C%5Bn%5D%5Ek = n%21%2F%28k%21%2A%28n-k%29%21%29 are binomial coefficients.



     Substituting given values into the formula, you get

         P(n=10, k=7, p= 0.55) = C%5B10%5D%5E7%2A0.55%5E7%2A%281-0.55%29%5E%2810-7%29 = %28%2810%2A9%2A8%29%2F%281%2A2%2A3%29%29%2A0.55%5E7%2A0.45%5E3 = 0.1665   (rounded).    ANSWER

Solved.

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If you want to see many similar  (or different)  solved problems,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
in this site.

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