A box contains 4 white ribbons and 8 pink ribbons.

Question

A box contains 4 white ribbons and 8 pink ribbons. Determine whether the events of picking a white ribbon and then another white ribbon without replacement are independent or dependent. Then identify the indicated probability.

 

Options:

 

 

independent; 1/11
	dependent; 1/12
	dependent; 1/11
	independent; 1/12

Answer 1

1) Two events are independent when one event happening (or not happening) does not affect the outcome of the other.

 

2) Getting a white (or pink) ribbon depends on the number of white (or pink) ribbons in the box as well as the total number of ribbons in the box.

 

3) When a ribbon is picked, and without replacing it, another ribbon is picked by random, the outcome of the event of picking the second ribbon gets affected as the number of ribbons has changed due to the first event.

 

4) The calculation of probability of getting a white ribbon is:

 

P(white) = Number of white in box / Total number of ribbons

 

5) To get another white ribbon in the second pick, we use the same formula as above with the numbers changed according to the outcome assumed in event one.

 

6) Now, since the second event depends on the first, the two probabilities get multiplied to give us the probability of happening both. The formal formula being:

 

P(AB) = P(A) * P(B) ; [only true for dependent events A and B]