# Conditional Probability and Rules of Probability

## High School Math Practice

This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

 Question Common Core Standard # 1 S.CP.1 2 S.CP.2 3 S.CP.3 4 S.CP.1 5 S.CP.4 6 S.CP.7 7 S.CP.9 + 8 S.CP.6 9 S.CP.
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school S.CP standards required for all students, including the college and career ready students.

Question 1: A box contains 5 blue marbles, 4 red marbles and 6 green marbles. How many additional blue marbles must be added in the box so that the probability of randomly drawing a blue marble is 1/2?

Question 2: A set of two dice is rolled. What is the probability of both dice showing odd face values?

Questions 3,4 and 5: A new high end restaurant was added to a cruise ship and data was recorded during the first voyage after the restaurant was opened. The number of passengers that dined at the restaurant is shown in the table below:

 Room Type Passenger group Dined Did not dine Total Suite A 121 209 330 Room with balcony B 114 320 434 Room with window C 85 325 410 Room without window D 150 621 771 Total 470 1475 1945

Are the events "passenger dined at the new restaurant" and "passenger was in group B" independent?

The probability that passengers from categories B and C dined at the new restaurant is .
Write the probability with three significant digits after the decimal point.

If a passenger from the ship is selected at random, the probability that the passenger booked a room with balcony is .
Write the probability with three significant digits after the decimal point.

Question 6: The New York State Education Department selects a number of schools to evaluate the education level of different areas of the state. Suppose that school A has a 8% chance to be selected and school B has a 6% chance to be selected. What is the probability that school A or school B will be selected, if the chance of both schools being chosen is 2%?

Question 7: Two basketball teams play against each other five games. For each game, the probability that team A wins is 0.6. The probability that team A wins three games and B wins two games is approximately .

Question 8: Two cards are selected without replacement from a standard deck of 52 cards. Find which of the following choices approximates the probability of selecting two kings.
Recall that there are 4 kings in a deck of 52 cards.

Questions 9 and 10: The probability that an archer shoots an arrow into the bullseye of a target in 0.9. The archer shoots three arrows and the success of one attempt is independent of the other two. Find the probability that none of the arrows hit the bullseye and the probability that at least one arrow hits the bullseye.
In the table below make only two selections, one in each column.

 None of the arrows At least one arrow Probability 0.001 0.1 0.5 0.9 0.999

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