Calculate the following probabilities:

Question

A bag contains nine black and six white marbles. One marble at a time is drawn repeatedly; its color is noted, and then it is replaced in the bag before the next draw. This experiment is carried out ten times

 

[A] Eight black marbles and two white marbles are drawn.

 

[B] At least five white marbles are drawn.

 

[C] Fewer than four black marbles are drawn.

Answer 1

Prob of black 9/15 or .6

Prob of white 6/15 or .4

 

This is a binomial setting with n=10 and p(black marble)=.6  x= black marbles.

 

A) P(x=8)= 10C8 .6^8*.4*2 =0.1209

 

B) P(x=0)+P(1)+P(2)+P(3)+P(4)+P(5)

(From binomial table since a pain to do by hand)

.0001+.0016+.0106+.0425+.1115+.2007=0.367

C) P(x=0)+P(1)+P(2)+p(3)

.0001+.0016+.0106+.0425=0.0548