Question

A bag contains two blue marbles, two green marbles, and three purple marbles. You randomly select a marble from the bag then roll a standard six-sided number cube. Let A be the event that you select a green marble. Let B be the event that you roll a number less than 3. The P(A∩B)=0.0952. Calculate P(A), P(B). Explain and show how to use those two probabilities to determine if events A and B are independent. Are the events independent? Round each calculation to four decimal places.

Answer 1

Explanation:

P(A) = 2/7 = 0.2857

P(B) = 1/3 = 0.3333

If A and B are independent, then P(A∩B) = P(A)*P(B) = 0.2857*0.3333

= 0.0952 which is the same as given for P(A∩B).

So A and B are independent.

Answer 2

Explanation:

P(A) = Probability of drawing a green marble from a bag of two blue marbles, two green marbles, and three purple marbles

= 2 (green) / 7 (total of two, two and three)

= 2/7

P(B) = Probability of rolling a number less than 3 from a standard six-sided number cube

= 2 (1 and 2 less than 3) / 6 (1 through 6)

= 1/3

P(A) and P(B) are calculated to be two real numbers and do not depend on each other. So event A and B are independent.