> 
> **Problem:** On a game show contestants play a game by putting mini-golf balls from
>  a five yard distance. Every contestant gets three chances to make a
>  put. Assume that every contestant has an equal chance of 0.2 of
>  sinking a ball. The game is won, if at least one of the three balls
>  can be sunk.
> 
> 
> 

(a) What is the probability that a contestant wins this game? Which distribution
are you using and what are the parameters?
(b) How many contestants do you expect to see on average until the third one wins?
Which distribution are you using and what are the parameters?

I have a X-Bin(3,0.2)

then, P(win the game)=3C1 \*0.2 (1-0.2)^2 + 3c2 \* 0.2 \* (1-0.2)^1 +3c2 \* 0.2 ($$)^0=0.488

Point b): NB(3, 0.488) then E(y)=3/0.488=6.25

**I need help with this this point:**

> 
> (c) If 300 contestants line up to play this game, what is the
>  approximate probability that at least 150 of them win?
> 
> 
> 

I need to use normal? How? the book said the answer is 0.360