What is the probability that he will choose two raincoats of the same pattern?

Question

There are nine raincoats in size 6-8 on sale in the girl's department at Bloomingdale's. Three have tulips, four have bunnies, and two have hearts. Mack is in a rush and randomly chooses two raincoats for his twin nieces. What is the probability that he will choose two raincoats of the same pattern?

 

a.5/18
b.1/2
c.18/729
d.8/243

Answer 1

Two ways to solve this problem

1. Probability of selecting objects without replacements

2. Combinations.

 

1. Probability of selecting objects without replacements

P{Picking two raincoats of the same pattern}

=P {2 tullips} + P {2 bunnies} + P { 2 hearts}

=(3/9)(2/8) + (4/9)(3/8) + (2/9)(1/8)

=20/72

= 5/18

 

2. Combinations.

P{Picking two raincoats of the same pattern}

= (Ways to choose 2 out of 3 tullips + Ways to choose 2 out of 4 bunnies + Ways to choose 2 out of 2 hearts/

   (Ways to choose 2 out of 9 raincoats)

= [C(3, 2) + C(4 2) + C(2,2])/C(9,2)

=(3 + 6 + 1) / 36

=5/18.

 

Just pick the one that is easier for you to remember and use for future homework or test questions

 

Enjoy!