Math in Focus Binomial Probability (1 Viewer)

[goobi]

One bag contains 5 blue and 3 yellow balls and another bag contains 7 blue and 2 yellow balls.
A bag is chosen at random and a ball drawn out. The result is recorded, then the ball is placed back in the bag. If this is done 20 times, find the probability of drawing out 12 blue balls correct to 3 decimal places.

The answer provided is 0.113.

Can anyone please help me solve it?

Thanks!

 

[such_such]

The probability that it is green:

<a href="http://www.codecogs.com/eqnedit.php?latex==\frac{5}{8}\cdot \frac{1}{2}@plus;\frac{7}{9}\cdot \frac{1}{2}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=\frac{5}{8}\cdot \frac{1}{2}+\frac{7}{9}\cdot \frac{1}{2}" title="=\frac{5}{8}\cdot \frac{1}{2}+\frac{7}{9}\cdot \frac{1}{2}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex==\frac{101}{144}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?=\frac{101}{144}" title="=\frac{101}{144}" /></a>

Now,
n = 20
P(success)= P(green) = <a href="http://www.codecogs.com/eqnedit.php?latex=\frac{101}{144}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{101}{144}" title="\frac{101}{144}" /></a>

P(fail) = (not green) = <a href="http://www.codecogs.com/eqnedit.php?latex=\frac{43}{144}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{43}{144}" title="\frac{43}{144}" /></a>

<a href="http://www.codecogs.com/eqnedit.php?latex=P(x=12)=\binom{20}{12}(\frac{101}{144})^{12}(\frac{43}{144})^{8}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?P(x=12)=\binom{20}{12}(\frac{101}{144})^{12})(\frac{43}{144})^{8}" title="P(x=12)=\binom{20}{12}(\frac{101}{144})^{12})(\frac{43}{144})^{8}" /></a>

= 0.113