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Probability and Statistics
Lesson 15		 Probability
  Objectives/Vocab/Tips > Examples 1 | 2 | 3 > Practice: 1 | 2 | 3 > Reflection

Example 3:

An actor's wardrobe includes:

  • 1 red hat and 1 white hat
  • 1 blue shirt, 1 white shirt, and 1 green shirt
  • 1 pair of black pants and 1 pair of white pants

If the actor randomly grabs 1 hat, 1 shirt, and 1 pairt of pants from the dark closet and is unable to see the colors, what is the probability the actor will pick an outfit that is all-white?

Show how you determine:

  • the total number of possible outfits
  • the number of all white outfits
  • the probability

Here are a couple of ways to solve this problem.

Begin by being sure you understand the problem and what it is you need to find. You know that an actor has a wardrobe in a dark closet that he is unable to see the color of his clothes before he picks the clothes out. You have three items to answer, including the total number of possible outfits, the number of all-white outfits and the probability that the actor will pick an all-white outfit.

One way to solve this problem would be to make a simple table to show all the outcomes. This would also help you with your explanation of how you solved this problem. Let's begin by making a simple table:
Hats
Shirts
Pants
Red
Blue
Black
Red
Blue
White
Red
White
Black
Red
White
White
Red
Green
Black
Red
Green
White
White
Blue
Black
White
Blue
White
White
White
Black
White
White
White
White
Green
Black
White
Green
White

When making your table and showing the different possible outfit combinations you find the answers to all three questions you are looking for.

Another way you may find the probability the actor pulls out the white piece of his wardrobe. Using your probability formula you know the following:

  • hats - 1 white/2 possible hat outcomes = 1/2 that the hat will be white
  • shirts - 1 white/3 possible shirt outcomes = 1/3 that the shirt will be white
  • pants - 1 white/2 possible pant outcomes = 1/2 that the pants will be white

If you multiply the three probabilities you will find the probability that the actor will pick an all white outfit.

1/2 x 1/3 x 1/2 = 1/12
Therefore, you found that there is a 1/12 chance that the actor will pick an all white outfit.

Either way you use to find the answers, you are now ready to answer the three questions required for this problem. You found that there are a total number of 12 possible outfits that the actor could end up choosing from the closet. There is only one all-white outfit as your table and formulas showed you. Lastly, you find the probability of picking the all-white outfit by placing the number of possible all-white outfits, which is 1, over the total number of possible outfits the actor could choose, which is 12.

Therefore you found the probability of the actor choosing an all white outfit is 1/12. In order to receive all points for this problem, make sure you have answered all three questions for this problem.

Practice 1 >>

 

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