My Math Forum [ASK] Professional Goalkeeper

 Probability and Statistics Basic Probability and Statistics Math Forum

 March 17th, 2018, 06:28 PM #1 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 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, 06:51 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,311 Thanks: 1224 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, 02:37 AM #3 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry Okay, thank you.

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