Question

Starting in 2013, every guest staying at a Disney hotel is given a free magic band (a bracelet that has a computer chip that turns a bracelet into a hotel room key, parktickets, and dining plan meal card). Prof. K has a collection of 21 magic band bracelets from various trips over the years as listed below:

MAGIC BAND COLOR

NUMBER OF MAGIC BANDS

Red

7

Pink

1

Yellow

3

Blue

4

Orange

2

Purple

3

Pink

1

Gray

1

I. If perso grabs 3 random magic bands from the box containing her collection to wear on her next trip, what is the probability that she packs 3 red bands?

shhow all work

Answer 1

here total number of magic bands =21

number of red magic bands =7

therefore probability that she packs 3 red bands =P(first is red band)*P(2nd is red|first is red)*P(3rd is red|first 2 are red)

=(7/21)*(6/20)*(5/19)=210/7980 =21/798=1/38