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March 17th, 2018, 05:28 PM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,000 Thanks: 132 Math Focus: Trigonometry  [ASK] Professional Goalkeeper
A professional goalkeeper can fend off a penalty kick with the probability of $\displaystyle \frac{3}{5}$. In an event a kick is done 5 times. The probability of that goalkeeper being able to fend off those penalty kicks 3 times is .... A. $\displaystyle \frac{180}{625}$ B. $\displaystyle \frac{612}{625}$ C. $\displaystyle \frac{216}{625}$ D. $\displaystyle \frac{228}{625}$ E. $\displaystyle \frac{230}{625}$ Can someone give me a hint? 
March 17th, 2018, 05:51 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,099 Thanks: 1093 
Binomial distribution with parameters $n=5,~p=\dfrac 3 5$ $P[3] = \dbinom{5}{3}\left(\dfrac 3 5\right)^3 \left(\dfrac 2 5\right)^2 = \dfrac{216}{625}$, i.e. choice (c) 
March 18th, 2018, 01:37 AM  #3 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,000 Thanks: 132 Math Focus: Trigonometry 
Okay, thank you.


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