What is the probability that a participant will randomly select a bag containing a sandwich with mayonnaise.

Question

Bag lunches were provided to the participants of a meeting. The sandwiches in the bag lunches were either turkey, ham or beef with either mayonnaise or mustard. Based on the diagram, what is the probability that a participant will randomly select a bag containing a sandwich with mayonnaise.

(I chose "C" 1/3 if I'm wrong, how so?)

Turkey ------------ mayonnaise + mustard

Ham ----------------mayonnaise + mustard

Roast beef --------mayonnaise + mustard


A. 1/9

B. 1/6

C. 1/3

D. 1/2

Answer 1

Well, Bran, I don't usually eat either mayonnaise or mustard, but I'll assume that there are three meats and that they always have exactly one ("with either") of the toppings (it is important to determine the total number of possible outcomes).

 

So, it the meats are T, H, and M, and the toppings are 1 and 2, then the total possibilities (3*2) are:

T1

T2

H1

H2

R1

R2

 

O.K. if all of these possibilities are random, independent events (and they are) with equal probabilities (and they have that), then the probability of "randomly select a bag containing a sandwich with mayonnaise" is the ratio of the number of successful events over the total of possible events:

        successful / total

               3/6             (because 3 of the outcomes have a "1")

               1/2            (1 out of 2, or 50%)

               Ans. D