Probability with Combinations and Permutations Answers

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Information about the recycling drive at school is shown in the table. Let A be the event that the item pulled out of the recycling bin is a plastic bottle, and let B be the event that a tenth grader recycled that item.

Question illustration
A
A and B are independent events because P(A∣B) = P(A).
B
A and B are independent events because P(A∣B) = P(B).
C
A and B are not independent events because P(A∣B) ≠ P(A).
D
A and B are not independent events because P(A∣B) ≠ P(B).
2
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The two-way table shows the ages of the players on different soccer teams.Which statement is true?

Question illustration
A
The probability that a randomly selected player on Team A is 8 years old is .
Option A
B
The probability that a randomly selected 8-year-old player is on Team C is .
Option B
C
The probability that a randomly selected player on Team C is 10 years old is .
Option C
D
The probability that a randomly selected 10-year-old player is on Team B is .
Option D
3

Information about the students at Jackson High School is shown in the table.

Question illustration
A
Out of the 352 eleventh graders at the school, 173 of them are girls.
B
Out of the 511 boys at the school, 150 of them are tenth graders.
C
Out of the 523 tenth graders at the school, 173 of them are boys.
D
Out of the 376 girls at the school, 182 of them are eleventh graders.
4

A survey was taken of children between the ages of 7 and 12. Let A be the event that the person rides the bus to school, and let B be the event that the person has 3 or more siblings.Which statement is true about whether A and B are independent events?

Question illustration
A
A and B are independent events because P(A∣B) = P(A) = 0.12.
B
A and B are independent events because P(A∣B) = P(A) = 0.25.
C
A and B are not independent events because P(A∣B) = 0.12 and P(A) = 0.25.
D
A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.
5

Which statements are true? Select three options.

A
Milk was requested for 16 of the large-sized meal orders.
B
Soda was requested for 280 of the kids’ meal orders.
C
A juice box was requested for 82 of the regular-sized meal orders.
D
Sixty-three of the orders of soda came with a regular-sized meal.
E
A total of 124 large-sized meals were ordered.
7

The two-way table shows the medal count for the top-performing countries in the 2012 Summer Olympics.Which statement is true?

Question illustration
A
The probability that a randomly selected silver medal was awarded to Great Britain is .
Option A
B
The probability that a randomly selected medal won by Russia was a bronze medal is .
Option B
C
The probability that a randomly selected gold medal was awarded to China is .
Option C
D
The probability that a randomly selected medal won by the United States was a silver medal is .
Option D
8

A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 45, 20, 25, 90. The third column is labeled Y with entries 30, 10, 35, 75. The fourth column is labeled Z with entries 60, 25, 50, 135. The fifth column is labeled Total with entries 135, 55 110, 300.

Question illustration
A
C and Y are independent events because P(C∣Y) = P(Y).
B
C and Y are independent events because P(C∣Y) = P(C).
C
C and Y are not independent events because P(C∣Y) ≠ P(Y).
D
C and Y are not independent events because P(C∣Y) ≠ P(C).

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