Conditional probability questions and solution

Q1.A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class passed the first test. What percent of those who passed the first test also passed the second test?

 P(First and Second)	= 	0.25
P(First)	0.42
P(Second/First)=P(First and Second)/P(First)
=0.25/0.42=0.60=60%

Q2 . A jar contains black and white marbles. Two marbles are chosen without replacement. The probability of selecting a black marble and then a white marble is 0.34, and the probability of selecting a black marble on the first draw is 0.47. What is the probability of selecting a white marble on the second draw, given that the first marble drawn was black?

P(White|Black)=P(Black and White)/P(Black)
	 =  	0.34	/0.47  
     =  	0.72	   =  	72%

Q3 .The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday?

P(Absent|Friday)=	
=  	P(Friday and Absent)	/P(Friday)
=  	0.03/	 0.2 
=  	0.15	  =  	15%

Q4. At Kennedy Middle School, the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68. What is the probability that a student takes Spanish given that the student is taking Technology?

P(Spanish|Technology)	  =  	P(Technology and Spanish)	/P(Technology) =  	0.087/0.68	  =  	0.13
  

Q5 70% of your friends like Chocolate, and 35% like Chocolate AND like toffe . What percent of those who like Chocolate also like toffe. ?

P(toffe|Chocolate) 
= P(Chocolate and toffe) / P(Chocolate)

=0.35 / 0.7 = 50%
50% of your friends who like Chocolate also like
toffe.