Basic Probability Rules

A key ring has 12 keys, 3 of which open the house door. If two keys are randomly selected without replacement, what is the probability that neither key opens the door?

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(orange,green)

• 1/15

• 2/15

• 3/31

• 1/5

Two marbles are drawn from a container in such a way that the first marble drawn is replaced before selecting the second marble. Does the outcome of the first draw affect the outcome of the second?

• Yes

• No

A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn. Are the two events dependent or independent?

• Independent

• Dependent

Mary is a good student. The probability that she studies and passes her test is 3/5. If the probability that she studies is 8/9. What is the probability that she passes given that she studies? 

• 27/40

• 1.48

• .008

• .0593

Alex took two tests. The probability of him failing both tests is 0.4. The probability of him failing the first test is 0.2. What is the probability of Alex passing the second test given that he has passed the first test?

• 0.75

• 0.25

• 0.35

• 0.15

A bag contains 5 red marbles and 4 pink marbles. A marble is randomly drawn and then replaced. What is the probability the first marble is pink and the second is red?

• 26.9%

• 24.7%

• 20.0%

• 5%

A die is tossed. Find P(less than 5 l even). Express your answer as a decimal rounded to 4 decimal places.

A number is selected at random from the set {1, 2, 3, 4, 5, 6, 7, 8}. Find P(prime l odd). Express your answer as a decimal rounded to 2 decimal places.

The probability that a certain person will buy a shirt is 0.2, the probability that he will buy a coat is 0.3 and the probability that he will buy a shirt given that he buys a coat is 0.4. Find the probability that he will buy both a

shirt and a coat.

• 0.1

• 0.2

• 0.13

• 0.12