Question 1193948
.
A high school baseball player has a 0.307 batting average. In one game, he gets 5 at bats. 
What is the probability he will get at least 3 hits in the game?
~~~~~~~~~~~~~~~



            It is a standard binomial distribution problem.



<pre>
The number of trials is n=5;  the indexes of successful trials are k=3, 4, 5; 
the probability of success for each single individual trial is p = 0.307).


     The formula to calculate the probability is


         P = P(3) + P(4) + P(5) = P(n=5; k>=3; p=0.307) = {{{sum(C[5]^k*0.307^k*(1-0.307)^(5-k),k=3,5)}}} = {{{sum(C[5]^k*0.307^k*0.693^(5-k), k=3,5)}}}.


     To facilitate my calculations, I used online calculator at this site  https://stattrek.com/online-calculator/binomial.aspx

     It provides nice instructions  and  a convenient input and output for all relevant options/cases.


          The resulting number is P = 0.17246357389 = 0.1725  (rounded).    <U>ANSWER</U>
</pre>

Solved.


---------------


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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson>How to calculate Binomial probabilities with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson>Solving problems on Binomial distribution with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson>Solving problems on Binomial distribution with Technology (using online solver)</A> 

in this site.


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

which is your &nbsp;PRIMARY &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).