Disjoint and Independent Probability

Given the probabilities P(A) =0.4 and P(A∪B) =0.6, what is the probability P(B): If A and B are mutually exclusive? If A and B are independent?

• 0.2; 0.4

• 0.2; 0.33

• 0.33; 0.2

• 0.6; 0.33

If P(A) = 0.34 and P(A or B) = 0.71, which of the following is false?

• P(B) = 0.37, if A and B are disjoint.

• P(B) = 0.561, if A and B are independent.

• Cannot be determined if A and B are neither disjoint nor independent.

• P(A∣B)= 0.34, if A and B are independent.

P(Freshman or Pizza):

• 27/50

• 4/50

• 3/50

• 30/50

P(Pizza ∩ Water) =

• 62/182

• 120/400

• 58/400

• 140/400

A box contains 3 brand A batteries and 7 brand B batteries. 30% of brand A batteries are faulty and 40% of brand B batteries are faulty. A battery is selected at random and then checked to see if it is faulty. What is the probability that a not faulty brand A battery is selected?

• 0.21

• 0.09

• 0.28

• 0.25

• 1
• 2
• 3
• 4

P(Sandals|Pants):

• 4/20

• 6/15

• 1/2

• 2/7

A group of 125 pick up truck owners were asked what brand truck they owned and whether it had four-wheel drive. The results are given in the two-way table.
You randomly select one truck owner. Which one of the following is true about the events "Owner has a Chevy" and "Owner's truck has four-wheel drive"?

• These two events are mutually exclusive and independent. 

• These two events are mutually exclusive, but not independent. 

• These two events are not mutually exclusive, but they are independent.

• These two events are neither mutually exclusive nor independent.

What is P(not sport | Foreign language)?

• 23/37

• 14/23

• 14/37

• 3/23

At a California college, 19% of the students speak Spanish, 7% speak French, and 4% speak both languages.  A student is chosen at random from the college.  What is the probability that the student speaks Spanish if she speaks French?

• 0.220

• 0.211

• 0.040

• 0.571