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Represent and Determine Probability Questions

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The Represent and Determine Probability questions below are in the following grade level(s):
Grades: 7 9 10 College Continuing Education

A restaurant display case has the following tea bag selections and number of bags available for each kind.

Black Tea 15
Cinnamon 10
Green Tea 15
Lemon 4
Raspberry 6

What is the probability that a tea bag randomly selected from the case will be cinnamon?
1. $1/50$
2. $1/10$
3. $1/5$
4. $1/4$

A fair coin will be flipped 3 times. What is the probability that the coin will land on tails exactly once?
1. $1/8$
2. $1/3$
3. $3/8$
4. $5/8$

You are dealt two cards of the same suit. What are the odds of flopping a flush (3 cards of the same suit)?
- The odds of flopping a flush is 118 to 1.
  $11/50*10/49*9/48=990/117600=0.00842$
  $1/0.00842=118.76$

You are dealt an Ace and King of the same suit. What are the odds of flopping a Royal Flush (Queen, Jack, and Ten of the same suit)?
- The odds of flopping a Royal Flush are 1 to 19,599.
  
  ${::}^nC_k = {:n!:}/{:(n-r)!r!:} =$ ${:50!:}/{:(50!-3!)*3!:} = {:50*49*48:}/6 = 19,600$

Naruto, Sasuke, Sakura, and Ino work as volunteers at the local kennel. Naruto gives the dogs baths every 4 days; Sasuke cleans out cages every 6 days; Sakura feeds the animals in Section B every 2 days; and Ino helps the receptionist every 3 days. How many times in 12 weeks will all 4 helpers be at the clinic on the same day?
- 7 days

A class has 11 boys and 9 girls. Two of the students will be selected at random to serve on a committee. What is the probability that both of the selected students will be girls?
1. $72/400$
2. $18/95$
3. $81/380$
4. $81/121$

Evaluate ${::}^6P_3$
- ${::}^nC_k = {:n!:}/{:(n-r)!r!:} = {:6!:}/{:3!*3!:} = {:6*5*4:}/{:3!:} = 20$

Evaluate ${::}^6C_3$
- ${::}^nC_k = {:n!:}/{:(n-r)!r!:} = {:6!:}/{:3!*3!:} = {:6*5*4:}/{:3!:} = 20$

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