Review 14: Probability

A group of 500 randomly chosen drivers was polled. The poll asked drivers if they preferred a gasoline engine or a diesel engine and if they regularly carpool or do not. The results are recorded in the table.

Using the table, determine which of the following statements is true if someone from the group of people polled was chosen at random.

• The probability that the driver does not regularly carpool given that they prefer a gasoline engine is less than the probability that the driver prefers a gasoline engine given that they do not regularly carpool.

• The probability that the driver does not regularly carpool given that they prefer a gasoline engine is greater than the probability that the driver prefers a gasoline engine given that they do not regularly carpool.

• The probability that the driver does not regularly carpool given that they prefer a diesel engine is greater than the probability that the driver prefers a diesel engine given that they do not regularly carpool.

• The probability that the driver regularly carpools given that they prefer a gasoline engine is greater than the probability that the driver prefers a gasoline engine given that they regularly carpool.

A card is drawn from an ordinary deck of cards. What is the probability that the card is a king given that the card is red?

• P(K|R)=0.16

• P(K|R)=0.8

• P(K|R)=0.2

• P(K|R)=0.08

Brenda is rolling a six-sided die and flipping a coin. Complete each of the following sentences regarding the probabilities involved in these actions using reduced fractions.

Select the answers that are true.

• The probability of rolling a five is 1/6

• The probability of flipping the coin and it landing on heads is 1/2

• The probability of rolling a five and landing on heads is 1/12

• The events are dependent

In a bag of keys, there are 12 silver keys, 6 black keys, 10 copper keys, and 2 painted keys of various colors. One key is drawn out at random. What is the probability that the key that is drawn is silver or copper?

• $\frac{11}{15}$

• $\frac{2}{5}$

• $\frac{1}{3}$

• $\frac{3}{5}$

A bag contains six red marbles, nine green marbles, two blue marbles, and seven yellow marbles. If Lisa draws a random marble from the bag, what is the probability that it will be a red, green, or blue marble?

• 
  

  $\frac{17}{24}$
  

• $\frac{7}{24}$

• $\frac{17}{48}$

• $\frac{1}{8}$

A number is chosen at random from a set of whole numbers from 2 to 41. What is the probability that the chosen number is a composite number?

• 
  

  $\frac{3}{20}$
  

• $\frac{17}{20}$

• $\frac{27}{40}$

• $\frac{13}{40}$

At a birthday party, there are 2 gift boxes that are red, 7 gift boxes that are green, 4 gift boxes that are blue, and 11 gift boxes that are multi-colored sitting on a table. If one of the gift boxes falls off the table at random, what is the probability that the gift box will be green?

• 
  

  $\frac{1}{6}$
  

• $\frac{7}{24}$

• $\frac{7}{17}$

• $\frac{1}{12}$

Bethany's class took a field trip to an amusement park. During the day Bethany became separated from her class. It is now time to leave, and she needs to find the right bus to get on to go back to school. Bethany attends Washington Elementary. In the parking lot, there are 4 buses from Washington Elementary, 5 buses from Adams Elementary, and 8 buses from Jefferson Elementary. Unfortunately, all these buses look alike. If Bethany goes up to a bus at random, what is the probability that it will be the wrong bus?

• 
  

  $\frac{4}{13}$
  

• $\frac{13}{17}$

• $\frac{4}{17}$

• $\frac{9}{17}$

Ross is rolling two 12-sided dice for a game. The probability that he will roll an even number and then a twelve is  $\frac{1}{24}$ 
Using this probability, determine if the event of rolling an even number and the event of rolling a twelve was independent, dependent, both, or neither.

• both independent and dependent

• neither independent nor dependent

• independent

• dependent

 A bag of marbles contains three red marbles, seven blue marbles, four green marbles, and five yellow marbles. The probability of Tyler drawing one yellow marble and then one green marble is  $\frac{10}{171}$ .

Using this probability, determine if the event of drawing a yellow marble on the first draw and the event of drawing a green marble on the second draw are independent, dependent, both, or neither.

• independent

• dependent

• both independent and dependent

• neither independent nor dependent