Question

Josh is the proud owner of an eclectic bow tie collection. He keeps track of how many bow ties he has, and organizes them by pattern and material.
Velvet Cotton
Zigzags 6 3
Swirls 3 3
What is the probability that a randomly selected bow tie is made of velvet given that the bow tie is designed with swirls?
Round to the nearest hundredth.

Answer 1

50%
Short Explanation:
Since we are given that the bowtie is designed with swirls, we can limit the possible choices only to the bowties with swirls (6) and since there are 3 bowties made of velvet out of those 6 we can conclude that 3/6 = 1/2 or 50%


Long Explanation:

P(A|B) = P(A and B)/ P(B)
P(A and B) is the probablity that a random bowtie is made of velvet multiplied by the probablilty that a random bowtie is designed with swirls.
This can be determined by taking the number of bowties with swirls made of velvet (3) and dividing that by the total number of bowties.
P(A and B) =(3/15)
P(B) is determined by the number of bowties with swirls divided by the total number of bowties
P(B) = 6/15
(3/15)/ (6/15) = 1/2 or 50%